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[tex]f(x)=4 x^{3}+a x^{2} +bx+c [/tex] 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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Konrad509idn
[tex]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}[/tex]
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