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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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Your Input

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 $$$2$$$.

Answer

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