Verify the condition of Rolle's theorem for the function y = f(x) = e xe[-1] ] f'(c) = 0 and find C for which

Q: 2. Find the derivative of a function at a certain number using the formula. f(x) – f(xo) f'(x) = lim…

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Q: Use definition to find derivative of the following function at z = 3 – 2i.

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Q: Show that the function f(t) = sin(e*) is of exponential order as t → +oo but that its derivative is…

A: To show that the given function ft=sinet2 is of exponential order.

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: C. Differentiation. Use the theorems in differentiation to solve for the derivative of the…

A: As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly repost…

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: 5. Consider the function f(x). f(x) = (2x² + 3x + 1 |x| sin(x - 1) + 1 if x < -1 if -1 < x < 1 if 1…

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Q: Suppose the function f and its derivative ƒ' have values as given in the following table. f(x) f'(x)…

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Q: a) Differentiate the function below with respect to x. 3+7x –3–52 f(x) = 33

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Q: What is the derivative of the following function

A: Given that: 1. h(y)=y1-ey2. f(t)=1+5tln(t)

Q: The nth derivatives of sinªx is ㅎ4"cos(4x +

A: FALSE. SOLUTION IS GIVEN BELOW HANDWRITTEN DOCUMENT. nth derivative of sin^4x

Q: Consider the following function. f(x) = x³ 3x² - 9x + 5 Find the first and second derivatives. f'(x)…

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Q: (d) Let h(x) g(f(x)). Use the figure below to find h'(1) or state why the derivative does not exist.…

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Q: 3. Consider the function f(x) = e¯*. 4x2 – 2 (a) Show that the second derivative is f"(x) (b) Find…

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Q: The sign x (t) is even symmetric and the sign y (t) is equal to the derivative of x (t). Show that…

A: even symmetric means it satisfies x(t)= x(-t) while odd symmetric means it satisfies x(-t)= -x(t)

Q: ) Use L(x) to approximate f(16.1).

A: For a given function f(x) the linearization at a point x=a is denoted by L(x) and it is defined as…