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13. The graph of f is shown. State, with reasons, the numbers at which f is not continuous. a) State, with reasons, the numbers at which fis not differentiable. b) 246 0 4 14. Trace the graph of...
8. Trace the graph of the function and sketch a graph of its derivative directly beneath b) a) c)...
8. Trace the graph of the function and sketch a graph of its derivative directly beneath b) a) c) Use any differentiation formulas to find equations of the tangent line and normal line to the curve y at the given point P a) y (2x -3)2 at P (1,1) b) y (2+x at P (0,2) 9. 10. The graph of f is shown. a) State, with reasons, the numbers at which f is not continuous. b) State, with reasons, the...
Graph of A continuous function fis defined on the closed interval - 4sxs6. The graph of...
Graph of A continuous function fis defined on the closed interval - 4sxs6. The graph of consists of a line segment and a curve that is tangent to the x-axis at x-3, as shown in the figure above. On th interval Dexc6, the function fis twice differentiable, with f(x)>0. Is there a value of a -4sach, for which the Mean Value Theorem applied to the interval (a 6), guarantees a value ca cx6, at which f'(c) = ? Justify your...
5. This problem concerns a function , about which the following information is known . fis a differentiable function defined at every real number x. y-f'(x) has its graph given in the m...
5. This problem concerns a function , about which the following information is known . fis a differentiable function defined at every real number x. y-f'(x) has its graph given in the middle picture below S. This problem concerns a function f, about which the following information is f is a differentiable function defined at every real number x. y(x) has its graph given in the middle picture below. Construct a first derivative sign chart for f. Clearly identify all...
15-16 The graph of the derivative f' of a continuous function f is shown. (a) On...
15-16 The graph of the derivative f' of a continuous function f is shown. (a) On what intervals is f increasing? Decreasing? (b) At what values of x does f have a local maximum? Local minimum? (c) On what intervals is f concave upward? Concave downward? (d) State the x-coordinate(s) of the point(s) of inflection. (e) Assuming that f(0) = 0, sketch a graph of f. 15. y A y = f'(x) --2 0 2 6 8 x -2
real analysis 1,2,3,4,8please 5.1.5a Thus iff: I→R is differentiable on n E N. is differentiable on / with g'...
real analysis
1,2,3,4,8please
5.1.5a
Thus iff: I→R is differentiable on n E N. is differentiable on / with g'(e) ()ain tained from Theorem 5.1.5(b) using mathematical induction, TOu the interal 1i then by the cho 174 Chapter s Differentiation ■ EXERCISES 5.1 the definition to find the derivative of each of the following functions. I. Use r+ 1 2. "Prove that for all integers n, O if n is negative). 3. "a. Prove that (cosx)--sinx. -- b. Find the derivative...
Suppose that a continuous function f has a derivative f' whose graph is shown below over...
Suppose that a continuous function f has a derivative f' whose graph is shown below over the interval (1, 10). y=f'(x) 1 2 3 4 5 6 8 9 10 (a) Find the interval(s) over which f is increasing. (Enter your answer using interval notation.) Find the interval(s) over which fis decreasing. (Enter your answer using interval notation.) (b) Find the x-value(s) where f has a local maximum. (Enter your answers as a comma-separated list.) x = Find the x-value(s)...
the function y=f(x)={ 0-4), 14x+16, x20 x<0 Consider 1. (a) Sketch the graph off. (3 pts.) (b) Verify that the function is continuous everywhere using the properties of the definition and poss...
the function y=f(x)={ 0-4), 14x+16, x20 x<0 Consider 1. (a) Sketch the graph off. (3 pts.) (b) Verify that the function is continuous everywhere using the properties of the definition and possibly calculating the limit at a particular point. (2 pts.) (c) Show f'(x) is not continuous at x-0. (5 pts.)
the function y=f(x)={ 0-4), 14x+16, x20 x
13) Consider the function f(, y)-4x2 +y a) Sketch a graph of level curves for fox.y)-4,8 and 16 (they should be ellipses) in xa-plare b) Calculate the gradient of f at the point (1,2). c) Find a d...
13) Consider the function f(, y)-4x2 +y a) Sketch a graph of level curves for fox.y)-4,8 and 16 (they should be ellipses) in xa-plare b) Calculate the gradient of f at the point (1,2). c) Find a direction (expressed as a unit vector) for which the directional derivative at the point (1,2) is 0.
13) Consider the function f(, y)-4x2 +y a) Sketch a graph of level curves for fox.y)-4,8 and 16 (they should be ellipses) in xa-plare b) Calculate...
For problems 8-12, use the graph of y=f(x) and the table for g(x) and g'(x) to...
For problems 8-12, use the graph of y=f(x) and the table for g(x) and g'(x) to compute the indicated derivatives. Write your final answer and only your final answer) in the space provided. Answers should be exact and fractions should be used where appropriate (do not use numbers in decimal form). 1 -4 -2 g(x) 2 5/2 3 14/5 &'(x) 7/5 1/2 1/4 -1/4 0 2 قيا 2 - 1 -2 - 1/2 4 0 5 6 8 1 6...
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) -...
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) - $(3) X-3 f(x)- $(3) (c) Find lim X-3 (d) Find and simplify $(3+h)-f(3) h 13 (e) Find lim f(3+h) – S (3) h 0 h (t) Find the slope-intercept form of the tangent line to y = f(x) at x = 3. (g) Plot the curve and the tangent line on the same graph, using the form on the window (-3,7]*[-10,10). 5. A car...
8. Trace the graph of the function and sketch a graph of its derivative directly beneath b) a) c) Use any differentiation formulas to find equations of the tangent line and normal line to the curve y at the given point P a) y (2x -3)2 at P (1,1) b) y (2+x at P (0,2) 9. 10. The graph of f is shown. a) State, with reasons, the numbers at which f is not continuous. b) State, with reasons, the...
Graph of A continuous function fis defined on the closed interval - 4sxs6. The graph of consists of a line segment and a curve that is tangent to the x-axis at x-3, as shown in the figure above. On th interval Dexc6, the function fis twice differentiable, with f(x)>0. Is there a value of a -4sach, for which the Mean Value Theorem applied to the interval (a 6), guarantees a value ca cx6, at which f'(c) = ? Justify your...
5. This problem concerns a function , about which the following information is known . fis a differentiable function defined at every real number x. y-f'(x) has its graph given in the middle picture below S. This problem concerns a function f, about which the following information is f is a differentiable function defined at every real number x. y(x) has its graph given in the middle picture below. Construct a first derivative sign chart for f. Clearly identify all...
15-16 The graph of the derivative f' of a continuous function f is shown. (a) On what intervals is f increasing? Decreasing? (b) At what values of x does f have a local maximum? Local minimum? (c) On what intervals is f concave upward? Concave downward? (d) State the x-coordinate(s) of the point(s) of inflection. (e) Assuming that f(0) = 0, sketch a graph of f. 15. y A y = f'(x) --2 0 2 6 8 x -2
real analysis
1,2,3,4,8please
5.1.5a
Thus iff: I→R is differentiable on n E N. is differentiable on / with g'(e) ()ain tained from Theorem 5.1.5(b) using mathematical induction, TOu the interal 1i then by the cho 174 Chapter s Differentiation ■ EXERCISES 5.1 the definition to find the derivative of each of the following functions. I. Use r+ 1 2. "Prove that for all integers n, O if n is negative). 3. "a. Prove that (cosx)--sinx. -- b. Find the derivative...
Suppose that a continuous function f has a derivative f' whose graph is shown below over the interval (1, 10). y=f'(x) 1 2 3 4 5 6 8 9 10 (a) Find the interval(s) over which f is increasing. (Enter your answer using interval notation.) Find the interval(s) over which fis decreasing. (Enter your answer using interval notation.) (b) Find the x-value(s) where f has a local maximum. (Enter your answers as a comma-separated list.) x = Find the x-value(s)...
the function y=f(x)={ 0-4), 14x+16, x20 x<0 Consider 1. (a) Sketch the graph off. (3 pts.) (b) Verify that the function is continuous everywhere using the properties of the definition and possibly calculating the limit at a particular point. (2 pts.) (c) Show f'(x) is not continuous at x-0. (5 pts.)
the function y=f(x)={ 0-4), 14x+16, x20 x
13) Consider the function f(, y)-4x2 +y a) Sketch a graph of level curves for fox.y)-4,8 and 16 (they should be ellipses) in xa-plare b) Calculate the gradient of f at the point (1,2). c) Find a direction (expressed as a unit vector) for which the directional derivative at the point (1,2) is 0.
13) Consider the function f(, y)-4x2 +y a) Sketch a graph of level curves for fox.y)-4,8 and 16 (they should be ellipses) in xa-plare b) Calculate...
For problems 8-12, use the graph of y=f(x) and the table for g(x) and g'(x) to compute the indicated derivatives. Write your final answer and only your final answer) in the space provided. Answers should be exact and fractions should be used where appropriate (do not use numbers in decimal form). 1 -4 -2 g(x) 2 5/2 3 14/5 &'(x) 7/5 1/2 1/4 -1/4 0 2 قيا 2 - 1 -2 - 1/2 4 0 5 6 8 1 6...
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) - $(3) X-3 f(x)- $(3) (c) Find lim X-3 (d) Find and simplify $(3+h)-f(3) h 13 (e) Find lim f(3+h) – S (3) h 0 h (t) Find the slope-intercept form of the tangent line to y = f(x) at x = 3. (g) Plot the curve and the tangent line on the same graph, using the form on the window (-3,7]*[-10,10). 5. A car...
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