SOLUTION: solve f´(2) if f(x) = x^3 - 6x^2 + 9x + 3 Determine the largest and smallest value of the function in the interval 0 ≤ x ≤ 5 with derivatives.

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Question 1156158: solve f´(2) if f(x) = x^3 - 6x^2 + 9x + 3
Determine the largest and smallest value of the function in the interval 0 ≤ x ≤ 5 with
derivatives.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

solve f´%282%29 if f%28x%29+=+x%5E3+-+6x%5E2+%2B+9x+%2B+3
f´%28x%29+=+3x%5E2+-+12x+%2B+9
f´%282%29+=+3%2A2%5E2+-+12%2A2+%2B+9
f´%282%29+=+12+-+24+%2B+9
f´%282%29+=+21+-+24+
f´%282%29+=++-+3

Determine the largest and smallest value of the function in the interval 0+%3C=+x+%3C=+5+with derivatives.
Check for local minimums or maximums by setting f'%28x%29 equal to 0.
0+=+3x%5E2+-12x+%2B+9........simplify, both sides divide by 3
0+=+x%5E2-4x+%2B+3....factor
0+=+%28x+-1%29+%28x+-3%29
x+=+1 or x=3
Evaluate f%28x%29 at the critical values, and at the end points.
f%280%29+=+3
f%281%29+=+7
f%283%29+=+3
f%285%29+=+23
f%28x%29 has a minimum of 3+and a maximum of 23.