SOLUTION: Determine the values of the constants a and b so that the function f ( x )= x3 + ax2 + bx + 5 may have a relative maximum at x= -3 and a relative minimum at x= 1

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Question 1113064: Determine the values of the constants a and b so that the function f ( x )= x3 + ax2 + bx + 5 may have a relative maximum at x= -3 and a relative minimum at x= 1
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


f ( x )= x^3 + ax^2 + bx + 5

f'(x) = 3x^2 + 2ax + b

The derivative is 0 where there are maxima or minima -- at x=-3 and x=1:

3%28-3%29%5E2%2B2a%28-3%29%2Bb+=+27-6a%2Bb+=+0
3%281%29%5E2%2B2a%281%29%2Bb+=+3%2B2a%2Bb+=+0
27-6a%2Bb+=+3%2B2a%2Bb
27-6a+=+3%2B2a
24+=+8a
a+=+3
3%2B2%283%29%2Bb+=+0
9%2Bb+=+0
b+=+-9

The function is f(x) = x^3 + 3x^2 - 9x + 5. A graph:

graph%28200%2C300%2C-6%2C3%2C-10%2C40%2Cx%5E3+%2B+3x%5E2+-+9x+%2B+5%29