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For the following equation, what is the instantaneous rate of change at
x=-1?

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

For the following equation, what is the instantaneous rate of change at $x=-1 ?$ $\newline$ $f(x)=-3 x^{2}+2$ $\newline$ 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=-1 ?

\newline

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

\newline

Answer:

Calculate Derivative: To find the instantaneous rate of change of the function at a specific point, we need to calculate the derivative of the function. The derivative of a function gives us the slope of the tangent line at any point, which is the instantaneous rate of change.
Apply Power Rule: The function given is $f(x) = -3x^2 + 2$ . To find its derivative, we use the power rule, which states that the derivative of $x^n$ is $n\cdot x^{(n-1)}$ . Applying this rule to each term in the function, we get: $\newline$ $f'(x) = \frac{d}{dx}(-3x^2) + \frac{d}{dx}(2)$ $\newline$ $f'(x) = -3 \cdot 2x^{(2-1)} + 0$ $\newline$ $f'(x) = -6x$
Find Instantaneous Rate: Now that we have the derivative, we can find the instantaneous rate of change at $x = -1$ by plugging $-1$ into the derivative function. $\newline$ $f'(-1) = -6*(-1)$ $\newline$ $f'(-1) = 6$

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