having serious problems finding the answer to this..
let f(x)= 3x^4-4x^3-12x^2+14

a.) use the first derivative to find exact values of all critical points and identify each critical point as a local minima, local maxima, or neither

b) use the second derivative to find exact values of all inflection points of f(x)

Question

having serious problems finding the answer to this..
let f(x)= 3x^4-4x^3-12x^2+14

a.) use the first derivative to find exact values of all critical points and identify each critical point as a local minima, local maxima, or neither

b) use the second derivative to find exact values of all inflection points of f(x)

anonymous · Answer

$$f \prime(x)= 12x^{3}-12x ^{2}-24x =12x(x ^{2}-x-2) =12x(x+1)(x-2)=0$$
The values of x are: 0.-1,2
$$f \prime \prime (x) = 36x ^{2}-24x-24=0  \to 3x ^{2}-2x-2=0 $$