Question

Given a function y = (–4x3 + 3x2 + 12x + 1). The value of 'x' for which the function 'y' has a maximum value is ?

Answer 1

Explanation:

y′

=6x 2−42x+36=0.. For critical point

Or

6(x 2−7x+6)=0

6(x−1)(x−6)=0

x=1 and x=6.

Now

f"(x)

=12x−42

For minima.

f"(x)>0

or

7

x> __

2

Or

x>3.5

Hence we get the minima at x=6.

Now

f(6)

=2(216)−21(36)+36(6)−20

=−128.