How do you find the instantaneous rate of change of the function $f(x)=x^2+2x$ when x=0?

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Answer 1 · 2018-03-03T06:13:31

$2$ .

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, $f(x)=x^2+2x$

And so $f'(x)$ is:

According to the power rule, $d/dxx^n=nx^(n-1)$ . We can now, using this, say:

$f'(x)=2x+2$ . 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 $2$ .

How do you find the instantaneous rate of change of the function f(x)=x^2+2xf(x)=x^2+2x when x=0?