\(f(x)=4 x^{3}+a x^{2} +bx+c\) and there is a local min at x=-1 and an inflection point at x=-2. Find the values of a and b

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26-01-2015
Mathematics

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\(f(x)=4 x^{3}+a x^{2} +bx+c\) and there is a local min at x=-1 and an inflection point at x=-2. Find the values of a and b

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konrad509 konrad509 · Answer 1 · 2015-01-26T17:57:39-05:00

konrad509 konrad509

26-01-2015

\(f'(x)=12x^2+2ax+b\\ 0=12\cdot(-1)^2+2a\cdot(-1)+b\\ 0=12-2a+b\\\\ f''(x)=24x+2a\\ 0=24\cdot(-2)+2a\\ 2a=48\\ a=24\\\\ 0=12-48+b\\ b=36\\\\ \boxed{a=24,b=36}\)

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