Determine f such that f ′′(x) = 6x − 6 and 2 is both a critical number and an x intercept of f.

Answer 1

f'(x)=3x²-6x+C

When x=2, f'(x)=0 means C=0

f(x)=x³-3x²+D

f(x)=0 => D=4

i.e. f(x)=x³-3x²+4