Question

For the function f(x) = 4x³ + 3x² – 6x + 1 find the intervals of monotonicity, local extrema, intervals of concavity and points of inflection.

Answer 1

4x³ + 3x² – 6x + 1

f'(x) = 12x² + 6x – 6 

f”(x) = 24x + 6 

f'(x) = 0 ⇒ 6(2x² + x – 1) = 0 

6(x + 1)(2x – 1) = 0

From (1) and (2) 

x = -1 is a maximum point, 

and f(-1)= -4 + 3 + 6 + 1 = 6 

So local maximum is 6

So local minimum is -3/4

of inflection is ((-1/4),(21/8))