Question

What is the instantaneous rate of change of `f(x)=sqrt(3x^2+4x+2)` at `x=4`?

Answer 1

`f'(4)=28/(2sqrt66)=1.72328`.

Explanation:

The instantaneous rate of change at a point is equivalent to the derivative evaluated at that point.
We evaluate this derivative by using the power rule.

`therefore f'(x)=d/dx(3x^2+4x+2)^(1/2)`

`=1/2(3x^2+4x+2)^(-1/2)*(6x+4)`

`therefore f'(4)=(6(4)+4)/(2sqrt((3(4^2)+4(4)+2)))=28/(2sqrt66)=1.72328`.