Q. 165.0( 1 Vote )

# Find the interval

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

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