Prove that if f (0) = g(0) and f' (x) ≤ g' (x) for x ≥ 0, then f (x) ≤ g(x) for all x ≥ 0. Hint: Show that the function given by y = f (x) − g(x) is nonincreasing.

Q: 2. Let f be defined by { x 0. f(x):= I 0 Using the definition of the derivative, verify if f has a…

A: We need to find derivative.

Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: 1. Sketch a function f(x) with the following properties: • f'(x) > 0 and f"(x) = 0, for x 2

A: As you posted multiple question , I need to solve only first question.

Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

A:

Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: 1. Let f(x)=√x-2 / x-4 . Show that f(x) has a removablediscotuiti t x=4   2. Given f(x)= √(x+1).…

A: Here we have to find the derivative of a function at a point.

Q: Let Compute f'(2). ƒ(x) = x³ + 3ª

A: This is a problem related to differentiation of the function. Please follow the procedure given…

Q: Let f(x) ∈ R[x]. Suppose that f(a) =0 but f'(a) ≠ 0, where f'(x) isthe derivative of f(x). Show that…

A:

Q: 2. Consider the function f(x) = e¯x -x5-x7 (a) Use the Intermediate Value Theorem to show that there…

A: We first recall definition of intermediate value theorem: if is a continuous function whose domain…

Q: d Suppose that f(x) and g(x) are differentiable functions such that f(5) = 1, f'(5) = 7, g(5) = 2,…

A: The objective is to simplify the given differential equation.

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

A: