Assume that h: [a, 6²] → R is a continuous function and let G: [a, b] → R denote the following function, 2 G(a) = [** h(t)dt. a Show that G is differentiable and find its derivative.

Q: (v) Let f(x) = /2x – 1, for r > 0. Use the definition of the derivative to compute f'(x).

A:

Q: 3) Differentiation D: F[t] ---> F[t], is linear and satisfies Dt¹ = nt¹-1. It satisfies the usual…

A: (a) We have f(c) = 0 if and only if (t-c) divides f in F[t]. Thus, we can write f(t) = (t-c)g(t) for…

Q: Let f(x) = x – In x + 7. a. What is the domain of f? b. Find the derivative of f. c. Identify all…

A: the solution is following.

Q: Suppose F(x) is a differentiable function for all real numbers x. Evaluate the following derivative.…

A: We need to find the derivative of the function F(x^4) with respect to x.

Q: Exercise 5: For the following graphs, sketch a graph of the derivative (i.e., you are given f;…

A: Consider the given curve of f(x).

Q: Suppose that f(a) = f(b) = g(a) = g(b) = 0 and the second derivatives of f and g are continuous on…

A:

Q: Let f be the function with derivative defined by f'(x) = cos(x²) on the interval -2 < x <2. How many…

A:

Q: Let f be a function defined by the rule (2.0 In(x)) Compute the derivative and evaluate it at x =3.…

A:

Q: f(x) = 4√x + 2x1/2 – 8x-7/8 + x2 1 23 +2

A: The given function is fx=4x+2x12-8x-78+x2-1x3+2. Find the derivative of the given function. Here we…

Q: If f has a derivative at x = 2, then f is continuous at x = = 2. True False

A:

Q: A function f: R → R has a third order continuous derivative. Show that f(a) f'(a). f"(a). f"" (a) ≥…

A: Given f:ℝ→ℝ has a third order continuous derivative Case 1: Consider fx is even function f-x=fx…

Q: Let ƒ (x) E R[x]. Suppose that f(a) = 0 and f'(a) = 0, where f'(x) is the derivative o f(x). Show…

A: Since, fa=0, fx can be factorized as fx=x-angx where n is a positive integer and g(x) is another…

Q: Let z=6. Differentiate the function f(x) = 7x7 - 8x + z. The required derivative is f '(x) =

A: Please find attachment