GATE (TF) Textile 2017 Question Paper Solution | GATE/2017/TF/30

Question 30 (Textile Engineering & Fibre Science)

The function f(x) = x^3-3x^2-9x+10 is

(A)Increasing in the interval (1,\infty)
(B)Increasing in the interval (-\infty , 1)
(C)Decreasing in the interval (-1,3)
(D)Decreasing in the interval (-3,1)
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f(x) = x^3-3x^2-9x+10
For maxima ,minima-
x=-1 and 3
\frac{d^2f}{dx^2}=6\times -1-6=-12<0 at x=-1, this is condition of maxima
\frac{d^2f}{dx^2}=6\times 3-6=12>0 at x=3, this is condition of minima
So the function is decreasing in the interval (-1, 3) (Ans)

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