SOLUTION: f(x)=x^n+5x, where n is an integer. Find n given the f'(2)=17

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Question 1079382: f(x)=x^n+5x, where n is an integer. Find n given the f'(2)=17
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=x^n+5x
f'(x) = nx^(n-1) + 5
f'(2) = n*2^(n-1) = 12 -> n*2^n/2 = 12 -> n*2^n = 24
Recognizing that 24 = 3*2^3, we see that n must be equal to 3.
Ans: n = 3
Check: 3(2)^2 + 5 = 17