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

Question

`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

Answer 1

`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}`