Q. 165.0( 1 Vote )

Find the interval

Answer :

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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