If f'(x) = g'(x) on the interval (a, b), then f(x) = g(x) on (a, b). O True O False
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- Determine whether each of the following statements is true or false, and explain why. The chain rule is used to take the derivative of a product of functions.Determine whether each of the following statements is true or false and explain why. The derivative of a function exists whenever the function is continuous.Explain the relationship between the slope and the derivative of fx at x=a.
- Determine whether each of the following statements is true or false, and explain why. The derivative of a sum is the sum of the derivatives.Use the graph of f(x) to find the interval where f''(x) > 0. -5 -4 -3 -2 -1 3- 2- 2 -3₂ 4 T 5 A. (0,3) B. (-3,00) C. (0,00) D. (-3,3)Let f be a function with f(1) = 3 and f'(1) = 1. If g(x) a²+1 f(x)' then g'(1) = (A) 글 (B) 긍 (C) 를 (D) (E) 4 (A) (B) (c) (D) (E)
- Evaluate f''(c) at the point.f(x) = (x2 - 4)(x3- 2), c = 1Use the graph of f(x) to find the interval where f''(x) > 0. Ⓡ 3- 2- 1- ms -5 -4 -3 -2 -1 1 3 4 5 A. (0,00) B. (-3,00) C. (0,3) O D. (-3,3)Let h(x): = f(x) where f(-7)= 4, f'(-7)= 8, g(-7)= -2, and g'(-7) = -2. What is h'(-7)? g(x)' Provide your answer below: h'(-7)=