Question

determine the constants a, b, and c in order for the function f(x)=x^3+ax^2+bx+c to have a relative maximum at x=1 and a point of inflection at x=2. find a relative minimum of the function given the found values of a and b, provided that f(0)=6. please help and show all steps!

Answer 1

is this calc one?

Answer 2

yes

Answer 3

ha...good times...

Answer 4

you want f'(1) = 0 and (probably) f''(1) < 0 for x=1 to be a local max
and you want f''(2) = 0 for x = 2 to be a point of inflection.

Can you write down the derivatives, f'(x) and f''(x) ?