Home
Class 11
MATHS
Show that f(x) = (k-(1)/(k)-x)(4-3x^(2))...

Show that `f(x) = (k-(1)/(k)-x)(4-3x^(2))` where k is a positive constant, has one and only one maximum value and only one minimum value and their difference is `(4)/(9)(k+(1)/(k))^(3)`

Text Solution

Verified by Experts

The correct Answer is:
`(4)/(9)(k+(1)/(k))^(3)`
Promotional Banner

Topper's Solved these Questions

  • MAXIMA AND MINIMA

    AAKASH SERIES|Exercise Examples|3 Videos

  • MAXIMA AND MINIMA

    AAKASH SERIES|Exercise Advanced Analytical Solved Examples|20 Videos

  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-III|35 Videos

  • MEAN VALUE THEOREMS

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I (LEVEL-II (MORE THAN ONE CORRECT ANSWER TYPE QUESTIONS ) )|2 Videos

Similar Questions

Explore conceptually related problems

If x, y, k, m, n are positive and x + y = k, then find the maximum value of x^(m)y^(n) .

If f(x) =x-k/x has a maximum value at x=-2 , then k=

Find the value of k, if (ii) (k)/(x^(2)-4) = (1)/(x-2)-(1)/(x+2)

The value of k if the equation 2cosx +cos2kx=3 has only one solution is

For what values of k, f(x) = x-(k)/(x) has a maximum value at x = -2.

Let f_(k)(x)=(1)/(k)(sin^(k)x+cos^(k)x) where x in R and k ge1 , then f_(4)(x)-f_(6)(x) equals

If 1/(9-x^(2))=1/k[1/(3-x)+1/(3+x)] " then "k=