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For the following equation, what is the instantaneous rate of change at
x=-2?

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

For the following equation, what is the instantaneous rate of change at $x=-2 ?$ $\newline$ $f(x)=2 x^{2}-5$ $\newline$ 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=-2 ?

\newline

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

\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 $f(x) = 2x^2 - 5$ . 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 our function, we differentiate each term separately.
Find Derivative of Function: Differentiating the term $2x^2$ , we get $2 \times 2x^{2-1} = 4x$ . The constant term $-5$ has a derivative of $0$ , since the derivative of any constant is $0$ .
Substitute $x = -2$ : Now we have the derivative of the function, which is $f'(x) = 4x$ . To find the instantaneous rate of change at $x = -2$ , we substitute $-2$ into the derivative.
Calculate Instantaneous Rate of Change: Substituting $x = -2$ into $f'(x) = 4x$ , we get $f'(-2) = 4*(-2) = -8$ .
Calculate Instantaneous Rate of Change: Substituting $x = -2$ into $f'(x) = 4x$ , we get $f'(-2) = 4\times(-2) = -8$ .The instantaneous rate of change of the function $f(x)$ at $x = -2$ is $-8$ .

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