Question

Please help please I dont know how to do this

Answer 1

$f(x)=2x^2-3x+2$

To find the instantaneous rate of change:

1. Find the derivate of f(x):

$\begin{gathered} \frac{d}{dx}ax^n=a*nx^{n-1} \\ \\ \frac{d}{dx}a=0 \\ \\ \\ \frac{d}{dx}f(x)=2*2x^{2-1}-3x^{1-1}+0 \\ \\ \frac{d}{dx}f(x)=4x-3 \\ \\ f^{\prime}(x)=4x-3 \end{gathered}$

2. Evaluate the derivate of f(x) for x=0:

$\begin{gathered} f^{\prime}(0)=4(0)-3 \\ f^{\prime}(0)=0-3 \\ f^{\prime}(0)=-3 \end{gathered}$

The instantaneus rate of change at x=0 of f(x) is the value of the derivate f'(x) evaluated in x=0.

Then, the instantaneus rate of change at x=0 is -3