What is the instantaneous rate of change of

Asa Huang

Asa Huang

Answered question

2022-03-14

What is the instantaneous rate of change of f(x)=x3x2+3x at x=3?

Answer & Explanation

skuleborn2de

skuleborn2de

Beginner2022-03-15Added 5 answers

The instantaneous rate of change at some point is simply the derivative at that point. So to solve this problem, all we do is find the derivative of the function and evaluate it at x=3.
Finding the derivative is easy; we use the power rule:
f(x)=3x22x+3
Now we set x=3 and find f'(x):
f(3)=3(3)22(3)+3
f'(3)=27-6+3
f'(3)=24
Therefore our instantaneous rate of change at x=3 is 24. This means the function is increasing at a rate of 24 at x=3.

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