Consider the function f(x) = x^3-x^2-x-1.
By taking the first derivative of this function, you can find critical points exist when $x = -\dfrac{1}{3}$ x = -\dfrac{1}{3} and x=1.
Using the second derivative test, find the values of $f''\left(-\frac{1}{3}\right)$ f''\left(-\frac{1}{3}\right) and f''(1).
Choose the correct option/s from below regarding the local maxima and minima of this function.

Question

Consider the function f(x) = x^3-x^2-x-1.

By taking the first derivative of this function, you can find critical points exist when $x = -\dfrac{1}{3}$ x = -\dfrac{1}{3} and x=1.

Using the second derivative test, find the values of $f''\left(-\frac{1}{3}\right)$ f''\left(-\frac{1}{3}\right) and f''(1).

Choose the correct option/s from below regarding the local maxima and minima of this function.

Answer

f''\left(-\frac{1}{3}\right) > 0 . Hence there is a local minimum when   x=-\dfrac{1}{3} .

Answer

f''(1) =4 . Hence   f''(c) > 0   for critical value   c  and there is a local minimum when   x=1 .

Answer

f''\left(-\frac{1}{3}\right) =-3 . Hence   f''(c) < 0   for critical value   c  and there is a local maximum when   x=-\dfrac{1}{3} .

Answer

f''(1) < 0 . Hence there is a local maximum when   x=1 .

Answer

f''\left(-\frac{1}{3}\right) =-4 . Hence   f''(c) < 0   for critical value   c  and there is a local maximum when   x=-\dfrac{1}{3} .

Answer

f''(1) =3 . Hence   f''(c) > 0   for critical value   c  and there is a local minimum when   x=1 .

Crowdly