# Find the instantaneous rate of change for the function at the given value. f(x) = x^2 + 3x at x =...

## Question:

Find the instantaneous rate of change for the function at the given value.

{eq}f(x) = x^2 + 3x \; {/eq} at {eq}\; x = -1 {/eq}

## Instantaneous Rate of Change:

Suppose we are given the value of the function {eq}f(x) {/eq}.

To determine the instantaneous rate of change of the function {eq}f(x) {/eq} at the point {eq}x=a {/eq}, we must take its derivative, and then plug in {eq}x=a {/eq}.

Determine first the derivative of the given function:

{eq}\begin{align*} f(x) & = x^2 + 3x\\ f'(x) & = 2x+3\\ \end{align*} {/eq}

Plugging in...

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