# What is the instantaneous rate of change of f(x)=-2x^3+5 x^2+3x  at x=-2?

Jun 15, 2017

$x = - 41$

#### Explanation:

What you want to do first is find the derivative using the power rule.
The derivative is the instantaneous rate of change.

Which states:

$\frac{d}{\mathrm{dx}} {x}^{n} = n {x}^{n - 1}$

$\frac{d}{\mathrm{dx}} = - \left(3\right) 2 {x}^{3 - 1} + \left(2\right) 5 {x}^{2 - 1} + \left(1\right) 3 {x}^{1 - 1}$

Please keep in mind that ${x}^{1 - 1} = {x}^{0} = 1$

$\frac{d}{\mathrm{dx}} = - 6 {x}^{2} + 10 x + 3$

Now you plug in $x = - 2$

$- 6 {\left(- 2\right)}^{2} + 10 \left(- 2\right) + 3 = - 41$