JEE Main · 2019 · 08 Apr 2019 · Shift 1 · Application of Derivatives

S_{1}

and

S_{2}

are respectively the sets of local minimum and local maximum points of the function.

f (x) = 9 x^{4} + 12 x^{3} - 36 x^{2} + 25, x \in R

, then

Answer: (A)

Solution

Differentiate to find the turning points:

f^{'} (x) = 36 x^{3} + 36 x^{2} - 72 x = 36 x (x - 1) (x + 2)

, zero at

x = - 2, 0, 1

. Tracking the sign of

f^{'}

, it is negative before

- 2

, positive on

(- 2, 0)

, negative on

(0, 1)

and positive beyond

1

. The changes from

-

+

x = - 2

and

x = 1

mark local minima, while the change from

+

-

x = 0

marks a local maximum. Hence

S_{1} = {- 2, 1}

and

S_{2} = {0}

JEE Main · 2019 · 08 Apr 2019 · Shift 1 · Single correct option