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Question

If f(x) = x3 + ax2 + bx + c has a maximum at x= -1 and minimum at x=3. Determine a,b and c.

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Solution

Given:y=x3+ax2+bx+cdydx=3x2+2ax+bSince fx is at maximum at x=-1 and minimum at x=3, x=-1 and x=3 are the critical points. At x=-1:dydx=3-12+2a-1+b=0 3-2a+b=02a-b=3 ... 1At x=3:dydx=332+2a3+b=027+6a+b=0-6a-b=27 ... 2From eqs. 1 and 2, we geta=-3, b=-9 and cR

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