JEE Main | 2018Maxima and MinimaHard

Question

Let f(x) = x2 + 1x2 and g(x) = x - 1x x∈R - {-1, 0, 1}. If h(x) = f(x)g(x) then the local minimum value of h(x) is : 

Options

A.

-3

B.

-22

C.

22

D.

3

Solution

h(x) = x2+1x2x-1x=x-1x+2x-1x
when x - 1x>0⇒x-1x+2x-1x⩾22
so 22 will be local minimum value

Create a free account to view solution

View Solution Free
Topic: Maxima and Minima·Practice all Maxima and Minima questions

More Maxima and Minima Questions

If for a function f(x), f′(b) = 0, f″(b) = 0, f″′(b) > 0, then x = b is-...The maximum value of 5 sinx + 12cosx is-...If x be real, then the minimum value of f(x) = 3x +1 + 3 − (x + 1) is -...If P(x) = a0 + a1x2 + a2x4 + ....... + anx2n be a polynomial in x ∈ R with 0 < a1 < a2 < .... < an, th...On the interval [0, 1] the function x25 (1 - x)75 takes its maximum value at the point -...