Check the solution to "What is the instantaneous rate of change of..."

Aryanna Rowland

Answered question

2022-03-16

What is the instantaneous rate of change of

f (x) = (x^{2} - 3 x) e^{x}

at x=2?

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^{'} (x) = e^{x} \frac{d}{d x} [x^{2} - 3 x] + (x^{2} - 3 x) \frac{d}{d x} [e^{x}]

f^{'} (x) = e^{x} (2 x - 3) + e^{x} (x^{2} - 3 x)

f^{'} (x) = e^{x} (2 x + 3 + x^{2} - 3 x)

f^{'} (x) = e^{x} (x^{2} - x + 3)

f^{'} (2) = e^{2} (2^{2} - 2 + 3)

f^{'} (2) = 5 e^{2}

f^{'} (2) = 5 e^{2}

f^{'} (2) \approx 36.945

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?