The derivative of the function f(0) = 96x + 12x2 – 20x3 + 3x4 has three...
1. The function f has derivative f' where f' is increasing and twice differentiable. Selected values of f' are given in the table above. It is known that f(0) = 3. (a) For f'(x), the conditions of the Mean Value Theorem are met on the closed interval (0,3). The conclusion of the Mean Value Theorem over the interval (0,3) for f'(x) is satisfied at c = 1. Find f"(c). (b) Use a right Riemann sum with the three subintervals indicated...
Find the derivative of the following function. f(x) = (2x - 3)(3x4 +7x) f'(x) = 2(3x4 + 7x)+(2x - 3)(12x3 +7) f'(x) = 2 + (12x3 + 7) f'(x) = 2(12x3 + 7) f'(x) = 2(3x4 +7x) – (2x - 3)(12x3 + 7)
4pts 1) Find the second derivative of the function f(x) = 3x4 + 2Vx
Question 11 10 pts The derivative f'(2) of an unknown function f(x) has been determined as f'(x) = (x - 2)(+3)2. Use this derivative to find the intervals where the original function f is increasing/decreasing. Then find the x-values that correspond to any relative maximums or relative minimums of the original unknown function f(x). O no relative maximum; relative minimum at x=2 relative maximum at x=-3; no relative minimum O relative maximum at x=2; relative minimum at x=-3 relative maximum...
9. Sketch the graph of a function, using the given information a. Intercepts: (0, 0) and (4, 0) Local Minimum: (3,-27) Points of Inflection: (0, 0) and (2, -16) f(x) c0 over the interval (-0,3) f(x)>0 over the interval (3,) f (x)>0 over the intervals (-o,0) and (2,0) "(x) <0 over the interval (0, 2 b. Sketch a graph of a differentiable function /(x) over the closed interval [-2, /(-2)-f (7) -3 and f (4) 3. The roots of /(x)...
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)...
Suppose that a continuous function f has a derivative f' whose graph is shown below over the interval (4, 13). y=f'(x) 1 2 3 4 5 6 7 8 9 10 11 12 13 (a) Find the interval(s) over which f is increasing. (Enter your answer using interval notation.) (4, 6)U(7, 9) U (11, 13) Find the interval(s) over which f is decreasing. (Enter your answer using interval notation.) (6, 7) U (9, 11) (b) Find the x-value(s) where f...
1. Suppose that f(x) has a critical number at x=c, and f′′(c)=−10 By the Second Derivative Test, we conclude A. the test is inconclusive. B. x=c is an inflection point C. x=c is a local (relative) minimum D. x=c is a local (relative) maximum E. x=c is an absolute minimum Question 4 of 10 3 Points What follows is a numeric fill in the blank question with 2 blanks. Find the absolute maximum and minimum value of the function f(x)=0.5x^4+(4/3)x^3−3x^2+4...
0/3 POINTS PREVIOUS ANSWERS SCALCETS 4.3.005. The graph of the derivative f' of a function f is shown. 6 8 10 12 (a) on what interval is fincreasing? (Enter your answer using interval notation) On what intervals is f decreasing? (Enter your answer using interval notation.) (by At What values of x does have a local maximum or minimum? (Enter your answers as a comma-separated lista
USING THE SECOND DERIVATIVE CRITERIA FIND THE CRITICAL POINTS OF F (X) AND DETERMINE IF THEY ARE LOCAL MAXIMUM OR MINIMUM 3x4 – 8x3 + 6x2