Find the intervals in which the function f(x) = 3x⁴ - 4x³ - 12x² + 5 is

(a) strictly increasing

(b) strictly decreasing

OR

Find the equations of the tangent and normal to the curve x = a sin³ θ and y = a cos³ θ at

f(x) = 3x⁴ - 4x³ - 12x² + 5

f^’(x) = 12x³ – 12x² – 24x

= 12x (x² – x – 2)

= 12x (x(x-2)+1(x-2))

= 12x (x+1) (x-2)

Now f^’(x) = 0

12x (x+1) (x-2) = 0

⇒ x = 0, x = -1 and x =-2

∴ f is strictly increasing in (-1,0)∪(2,∞) and strictly decreasing in (-∞,-1)∪(0,2).

OR

The curve x = a sin³ θ and y = a cos³ θ….. (1)

At θ=π /4

Point is point for (1) at π/4.

Differentiating (1) w.r.t to θ we get,

cot θ

At π/4,

= -1

Slope at normal is 1.

Equation of tangent is:

Equation ofnormal is:

y=x