For the following equation, evaluate f^(')(3). f(x)=-x^(3)-4x Answer:

Identify Function and Point: Identify the function and the point at which the derivative is to be evaluated. We are given the function f(x) = -x^3 - 4x and we need to find the derivative of this function at x = 3.Calculate Derivative of Function: Calculate the derivative of the function f(x). To find f'(x), we need to differentiate f(x) with respect to x. f'(x) = d/dx (-x^3 - 4x) Using the power rule, the derivative of -x^3 is -3x^2, and the derivative of -4x is -4. So, f'(x) = -3x^2 - 4Evaluate Derivative at x=3: Evaluate the derivative at x = 3. Substitute x = 3 into the derivative f'(x) to find f'(3). f'(3) = -3(3)^2 - 4 f'(3) = -3(9) - 4 f'(3) = -27 - 4 f'(3) = -31

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For the following equation, evaluate
f^(')(3).

f(x)=-x^(3)-4x
Answer:

For the following equation, evaluate $f^{\prime}(3)$ . $\newline$ $f(x)=-x^{3}-4 x$ $\newline$ Answer:

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Algebra 2

Find the vertex of the transformed function

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Q. For the following equation, evaluate

f^{\prime}(3)

\newline

f(x)=-x^{3}-4 x

\newline

Answer:

Identify Function and Point: Identify the function and the point at which the derivative is to be evaluated. $\newline$ We are given the function $f(x) = -x^3 - 4x$ and we need to find the derivative of this function at $x = 3$ .
Calculate Derivative of Function: Calculate the derivative of the function $f(x)$ . To find $f'(x)$ , we need to differentiate $f(x)$ with respect to $x$ . $f'(x) = \frac{d}{dx} (-x^3 - 4x)$ Using the power rule, the derivative of $-x^3$ is $-3x^2$ , and the derivative of $-4x$ is $-4$ . So, $f'(x) = -3x^2 - 4$
Evaluate Derivative at $x=3$ : Evaluate the derivative at $x = 3$ . Substitute $x = 3$ into the derivative $f'(x)$ to find $f'(3)$ . $f'(3) = -3(3)^2 - 4$ $f'(3) = -3(9) - 4$ $f'(3) = -27 - 4$ $f'(3) = -31$