Question

How do you find the instantaneous rate of change of the function `x^3 +2x^2 + x` when x=1?

Answer 1

`8`

Explanation:

Find the value of the derivative at `x=1`:

To find the derivative of the function, use the power rule:

`f'(x)=3x^2+4x+1`

The instantaneous rate of change and slope of the tangent line at `x=1` is:

`f'(1)=3(1)^2+4(1)+1=8`