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For the following equation, what is the instantaneous rate of change at
x=3 ?

f(x)=x^(3)-2x-4
Answer:

For the following equation, what is the instantaneous rate of change at $x=3$ ? $\newline$ $f(x)=x^{3}-2 x-4$ $\newline$ Answer:

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Find derivatives using logarithmic differentiation

Full solution

Q. For the following equation, what is the instantaneous rate of change at

x=3

?

\newline

f(x)=x^{3}-2 x-4

\newline

Answer:

Calculate Derivative: To find the instantaneous rate of change of the function at $x = 3$ , we need to calculate the derivative of the function $f(x)$ with respect to $x$ and then evaluate it at $x = 3$ .
Evaluate Derivative at $x=3$ : The derivative of $f(x) = x^3 - 2x - 4$ with respect to $x$ is $f'(x) = 3x^2 - 2$ . This is because the derivative of $x^3$ is $3x^2$ , the derivative of $-2x$ is $-2$ , and the derivative of a constant like $-4$ is $0$ .
Substitute $x=3$ : Now we evaluate the derivative $f'(x)$ at $x = 3$ . So we substitute $x$ with $3$ in the derivative to get $f'(3) = 3(3)^2 - 2$ .
Calculate Instantaneous Rate: Calculating $f'(3)$ gives us $f'(3) = 3(9) - 2 = 27 - 2 = 25$ .

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