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

Identify Function & Derivative: Identify the function and the derivative to be calculated. We are given the function f(x) = -2x^3 + 2 and we need to find its derivative at x = 2, which is denoted by f'(2).Calculate Derivative of Function: Calculate the derivative of the function f(x). The derivative of f(x) = -2x^3 + 2 with respect to x is f'(x) = -6x^2. This is obtained by applying the power rule of differentiation, which states that the derivative of x^n is n*x^(n-1).Evaluate Derivative at x = 2: Evaluate the derivative at x = 2. Substitute x = 2 into the derivative f'(x) = -6x^2 to find f'(2). f'(2) = -6*(2)^2 f'(2) = -6*4 f'(2) = -24

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For the following equation, evaluate
f^(')(2).

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

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

\newline

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

\newline

Answer:

Identify Function & Derivative: Identify the function and the derivative to be calculated. $\newline$ We are given the function $f(x) = -2x^3 + 2$ and we need to find its derivative at $x = 2$ , which is denoted by $f'(2)$ .
Calculate Derivative of Function: Calculate the derivative of the function $f(x)$ . The derivative of $f(x) = -2x^3 + 2$ with respect to $x$ is $f'(x) = -6x^2$ . This is obtained by applying the power rule of differentiation, which states that the derivative of $x^n$ is $n\cdot x^{(n-1)}$ .
Evaluate Derivative at $x = 2$ : Evaluate the derivative at $x = 2$ . Substitute $x = 2$ into the derivative $f'(x) = -6x^2$ to find $f'(2)$ . $f'(2) = -6*(2)^2$ $f'(2) = -6*4$ $f'(2) = -24$