# How do you find the instantaneous rate of change of the function f ( x ) = x <

How do you find the instantaneous rate of change of the function $f\left(x\right)={x}^{2}+2x$ when x=0?
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Quinn Everett
To find the instantaneous rate of change of a function f(x) at a point d, we solve for f'(x), and then solve for f'(d).
Here, $f\left(x\right)={x}^{2}+2x$
And so f'(x) is:
According to the power rule, $\frac{d}{dx}{x}^{n}=n{x}^{n-1}$
f'(x)=2x+2. Here, d=0, so we input:
f'(0)=2*0+2
f'(0)=2
The rate of change of the function at x=0 is 2