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For the graphs below, sketch the graph of the
derivative.
(3) For the graphs below, sketch...
4. Look at the graph below of the derivative f' (a). From this, make a sketch...
4. Look at the graph below of the derivative f' (a). From this, make a sketch of the original function f(x) and of the second derivative f" (2x), and explain your reasoning. (7 marks) A
12. (8 points) A Graph Satisfying First and Second Derivative Conditions On the figure below, sketch...
12. (8 points) A Graph Satisfying First and Second Derivative Conditions On the figure below, sketch the graph of a function y = f(x) that satisfies: • f(-2) = -3, • f is continuous • F"(x) > 0 on (-00, 2). • f is concave up for 1 > 2, and • lim f(1) = -2. • f'(2) does not exist. 00
Sketch the graph of f and then sketch the graphs of the even and odd extensions of f of period
Let$$ f(x)= \begin{cases}x, & 0 \leqslant x<2 \\ 1, & 2 \leqslant x<3\end{cases} $$Sketch the graph of f and then sketch the graphs of the even and odd extensions of f of period T = 2L = 6. You may do this all on the same set of axes if you can clearly indicate the different graphs (for example, use different colors).
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...
The Graph Game Choose one of the graphs listed below. On a separate sheet of graph...
The Graph Game Choose one of the graphs listed below. On a separate sheet of graph paper, sketch the derivative of this graph. Make sure you remember what you've learned about local maxima, local minima, and concavity while you draw your graph. Every point on the derivative graph should correspond to the slope of the original function. Give your piece of graph paper with the derivative sketch to your partner group when you are done.
(a) A function / has first derivative f'(z) = and second derivative 3) f"(x) It is also known that the function...
(a) A function / has first derivative f'(z) = and second derivative 3) f"(x) It is also known that the function f has r-intercept at (-3,0), and a y-intercept at (0,0) (i) Find all critical points, and use them to identify the intervals over which you will examine the behaviour of the first derivative ii) Use the f'(), and the First Derivative Test to classify each critical point. (ii) Use the second derivative to examine the concavity around critical points...
Curve Sketching: Use the following guidelines to sketch the graph of y-f(x) x-5x (20 points) a. What are the behaviors of y when x->oo, or x--0? (3 points) b. What is the first derivative of t...
Curve Sketching: Use the following guidelines to sketch the graph of y-f(x) x-5x (20 points) a. What are the behaviors of y when x->oo, or x--0? (3 points) b. What is the first derivative of this function? What are increasing intervals and decreasing intervals and max points and mini points? (6 points) c. What are the second derivative of this function? What are intervals for concavity upwards and concavity downwards and inflection points? (6 points) Use the above information (a,...
function y = f(x) and its derivative y= f'(x), but whoever made these graphs forget to...
function y = f(x) and its derivative y= f'(x), but whoever made these graphs forget to label which one is which. First, describe the graphs of these functions. What are some key features of the graph? Imagine your are trying to describe the graph to someone who cannot see it. Which graph is the function and which one is the derivative? Explain in 100 words how you arrived at your answer.
Use the steps below to sketch the graph y = x^2 - 7x - 18. Required...
Use the steps below to sketch the graph y = x^2 - 7x - 18. Required points are the x intercepts and the max and mix of the graph 1. Determine the domain of f. 2. Find the x- and y-intercepts of f.† 3. Determine the behavior of f for large absolute values of x. 4. Find all horizontal and vertical asymptotes of the graph of f. 5. Determine the intervals where f is increasing and where f is decreasing....
Consider the polynomial f(x,y)=ax^2+bxy+cy^2 (without using second derivative test) by identifying the graph as a paraboloid. ***Graph at least 9 DIFFERENT polynomials. Show graphs to accompany ac...
Consider the polynomial
f(x,y)=ax^2+bxy+cy^2 (without using second derivative test) by
identifying the graph as a paraboloid.
***Graph at least 9 DIFFERENT
polynomials.
Show graphs to accompany actual
working. Would appreciate it dearly.
Quadratic Approximations and Critical Points Consider the polynomial f(x,y)+ ry+ c (without using the Second Derivative Tet) by identifying the graph as a paraboloid. 1. Graph f(x, y) for at least 9 different polynomials. (Specific choices of a, b and c.)
Quadratic Approximations and Critical Points Consider the...
4. Look at the graph below of the derivative f' (a). From this, make a sketch of the original function f(x) and of the second derivative f" (2x), and explain your reasoning. (7 marks) A
12. (8 points) A Graph Satisfying First and Second Derivative Conditions On the figure below, sketch the graph of a function y = f(x) that satisfies: • f(-2) = -3, • f is continuous • F"(x) > 0 on (-00, 2). • f is concave up for 1 > 2, and • lim f(1) = -2. • f'(2) does not exist. 00
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...
The Graph Game Choose one of the graphs listed below. On a separate sheet of graph paper, sketch the derivative of this graph. Make sure you remember what you've learned about local maxima, local minima, and concavity while you draw your graph. Every point on the derivative graph should correspond to the slope of the original function. Give your piece of graph paper with the derivative sketch to your partner group when you are done.
(a) A function / has first derivative f'(z) = and second derivative 3) f"(x) It is also known that the function f has r-intercept at (-3,0), and a y-intercept at (0,0) (i) Find all critical points, and use them to identify the intervals over which you will examine the behaviour of the first derivative ii) Use the f'(), and the First Derivative Test to classify each critical point. (ii) Use the second derivative to examine the concavity around critical points...
Curve Sketching: Use the following guidelines to sketch the graph of y-f(x) x-5x (20 points) a. What are the behaviors of y when x->oo, or x--0? (3 points) b. What is the first derivative of this function? What are increasing intervals and decreasing intervals and max points and mini points? (6 points) c. What are the second derivative of this function? What are intervals for concavity upwards and concavity downwards and inflection points? (6 points) Use the above information (a,...
Consider the polynomial
f(x,y)=ax^2+bxy+cy^2 (without using second derivative test) by
identifying the graph as a paraboloid.
***Graph at least 9 DIFFERENT
polynomials.
Show graphs to accompany actual
working. Would appreciate it dearly.
Quadratic Approximations and Critical Points Consider the polynomial f(x,y)+ ry+ c (without using the Second Derivative Tet) by identifying the graph as a paraboloid. 1. Graph f(x, y) for at least 9 different polynomials. (Specific choices of a, b and c.)
Quadratic Approximations and Critical Points Consider the...
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