For the following equation, evaluate f^(')(1). f(x)=-2x^(3)+5 Answer:

Identify Function and Derivative: Identify the function and the derivative to be evaluated. We are given the function f(x) = -2x^3 + 5 and we need to find its derivative f'(x) at x = 1.Calculate Derivative of Function: Calculate the derivative of the function f(x). The derivative of f(x) = -2x^3 + 5 with respect to x is f'(x) = d/dx(-2x^3) + d/dx(5). Using the power rule for differentiation, the derivative of -2x^3 is -6x^2. The derivative of a constant, 5, is 0. So, f'(x) = -6x^2 + 0, which simplifies to f'(x) = -6x^2.Evaluate Derivative at x = 1: Evaluate the derivative at x = 1. Substitute x = 1 into the derivative f'(x) = -6x^2. f'(1) = -6(1)^2 f'(1) = -6(1) f'(1) = -6

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For the following equation, evaluate
f^(')(1).

f(x)=-2x^(3)+5
Answer:

For the following equation, evaluate $f^{\prime}(1)$ . $\newline$ $f(x)=-2 x^{3}+5$ $\newline$ Answer:

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Algebra 2

Composition of linear and quadratic functions: find a value

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Q. For the following equation, evaluate

f^{\prime}(1)

\newline

f(x)=-2 x^{3}+5

\newline

Answer:

Identify Function and Derivative: Identify the function and the derivative to be evaluated. $\newline$ We are given the function $f(x) = -2x^3 + 5$ and we need to find its derivative $f'(x)$ at $x = 1$ .
Calculate Derivative of Function: Calculate the derivative of the function $f(x)$ . The derivative of $f(x) = -2x^3 + 5$ with respect to $x$ is $f'(x) = \frac{d}{dx}(-2x^3) + \frac{d}{dx}(5)$ . Using the power rule for differentiation, the derivative of $-2x^3$ is $-6x^2$ . The derivative of a constant, $5$ , is $0$ . So, $f'(x) = -6x^2 + 0$ , which simplifies to $f'(x) = -6x^2$ .
Evaluate Derivative at x = $1$ : Evaluate the derivative at $x = 1$ . $\newline$ Substitute $x = 1$ into the derivative $f'(x) = -6x^2$ . $\newline$ $f'(1) = -6(1)^2$ $\newline$ $f'(1) = -6(1)$ $\newline$ $f'(1) = -6$