3. (12) If the function below is continuous and differentiable everywhere within the interval [-3, 3),...
3. (12) If the function below is continuous and differentiable everywhere within the interval (-3, 3), sketch the graph which satisfies the following conditions: f(-3) = 0, f(-2) = 3, f(-1) = 2, f(1) = -1, S (3) = -2 f'(-2) = 0 f'(x) > 0 on (-3,-2), f '(x) <0 on (-2, 3) f"(x) > 0 on (-1, 1), f '(x) <0 on (-3,-1) (1, 3)
x2 +7x+12 1. Consider the function: f(x)= x +3 a. Is this function continuous at x = -3? b. Does this function have a limit at x = -3? dito c. Is this function differentiable at x = -3? d. Sketch a graph of the function in the space below. Be sure to include all pertinent features.
At x = 1 the function (in the graph below) is o continuous, differentiable o continuous, not differentiable o not continuous, not differentiable o not continuous, differentiable
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 a possible graph of a function that satisfies the conditions below. Determine whether fis continuous at x = 1. f(1) = 2; lim f(x) = -2; lim f(x) = 2 x=1 *1* Choose the correct graph below. OA. B. OC. D. ro х X х -5 5 -5 5 -5 5 -5 5 Is f(x) continuous at x = 1? No оо Yes
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...
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
QUESTION 4 Find the intervals on which the function is continuous. у зе continuous everywhere discontinuous only when discontinuous only when e discontinuous only when e QUESTION 5 Provide an appropriate response. Use a calculator to graph the function f to see whether it appears to have a continuous extension to the origin. If it does, use Trace and Zoom to find a good candidate for the extended function's value at x 0. If the function does the origin from...
Sketch the graph of a function that is continuous on (-0,ce) and satisfies the following sets of conditions. 4-6)=21-5-or(- = 0; f(-4)=1-4)= 0; f(-3)=P(-3)=0 Choose the correct answer below OA OB C. OD. o S
Question 6 (1 point) Suppose a function f(x) is differentiable everywhere and has a local minimum at x=c. If f(x)<O when x<c, and f'(x)>0 when x>c, then by the Global Interval Method we know x=c is O a local maximum an absolute maximum a local minimum an absolute minimum