# Instantaneous rate of change of $f{\left(x \right)} = x^{2} + 2 x$ at $x = 0$

The calculator will find the instantaneous rate of change of the function $f{\left(x \right)} = x^{2} + 2 x$ at the point $x = 0$, with steps shown.

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Find the instantaneous rate of change of $f{\left(x \right)} = x^{2} + 2 x$ at $x = 0$.

### Solution

The instantaneous rate of change of the function $f{\left(x \right)}$ at the point $x = x_{0}$ is the derivative of the function $f{\left(x \right)}$ evaluated at the point $x = x_{0}$.

This means that we need to find the derivative of $x^{2} + 2 x$ and evaluate it at $x = 0$.

So, find the derivative of the function: $\frac{d}{dx} \left(x^{2} + 2 x\right) = 2 x + 2$ (for steps, see derivative calculator).

Finally, evaluate the derivative at $x = 0$.

$\left(\frac{d}{dx} \left(x^{2} + 2 x\right)\right)|_{\left(x = 0\right)} = \left(2 x + 2\right)|_{\left(x = 0\right)} = 2$

Therefore, the instantaneous rate of change of $f{\left(x \right)} = x^{2} + 2 x$ at $x = 0$ is $2$.

The instantaneous rate of $f{\left(x \right)} = x^{2} + 2 x$A at $x = 0$A is $2$A.