What is the instantaneous rate of change of f(x)=(x2−3x)ex at x=2?

Aryanna Rowland

Answered question

2022-03-16

What is the instantaneous rate of change of $f\left(x\right)=({x}^{2}-3x){e}^{x}$ at x=2?

Answer & Explanation

orangepaperiz7

Beginner2022-03-17Added 9 answers

The instantaneous rate of change when x=2 can be found through computing f'(2). To find f'(2), first find f'(x) Use the product rule: ${f}^{\prime}\left(x\right)={e}^{x}\frac{d}{dx}[{x}^{2}-3x]+({x}^{2}-3x)\frac{d}{dx}\left[{e}^{x}\right]$ ${f}^{\prime}\left(x\right)={e}^{x}(2x-3)+{e}^{x}({x}^{2}-3x)$ ${f}^{\prime}\left(x\right)={e}^{x}(2x+3+{x}^{2}-3x)$ ${f}^{\prime}\left(x\right)={e}^{x}({x}^{2}-x+3)$ ${f}^{\prime}\left(2\right)={e}^{2}({2}^{2}-2+3)$ $f}^{\prime}\left(2\right)=5{e}^{2$ $f}^{\prime}\left(2\right)=5{e}^{2$ ${f}^{\prime}\left(2\right)\approx 36.945$