Home
Class 12
MATHS
Find the critical (stationary ) points o...

Find the critical (stationary ) points of the function f(X)=`(x^(5))/(20)-(x^(4))/(12)`+5Name these points .Also find the point of inflection

Text Solution

Verified by Experts

The correct Answer is:
Point of maxima x=0
Point of minima: `x=4//3` Point of inflection :x=1
f(x)=`(x^(5))/(20)-(x^(4))/(12)+5`
`therefore f(x)=(x^(4))/(4)-(X^(3))/(3)=(x^(3))/(12)(3x-4)`
sign scheme of f(x)

From the sign scheme x =0 is point of maxima and `x=4//3` is point minima
So , x =1 is point inflection
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.5|5 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.6|9 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.3|6 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|13 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Find the critical points(s) and stationary points (s) of the function f(x)=(x-2)^(2//3)(2x+1)

The critical points of the function f(x)=(x-2)^(2/3)(2x+1) are

Find the domain of the function f(x)=(x^(2)+3x+5)/(x^(2)-5x+4)

Find the critical number and stationary point f(x) = 2x - 3x^(2)

Find the points of discontinuity of the function: f(x)=1/(x^4+x^2+1)

Find the points of discontinuity of the function: f(x)=1/(2sinx-1)

Find the points of discontinuity of the function: f(x)=1/(1-e^((x-1)/(x-2)))

Find the points of discontinuity of the function: f(x)=1/(x^2-3|x|+2)

Find the domain of the function f(x) = (x^2 + 3x +5 )/( x^2 -5x+4)

Draw the graph of f(x) = e^(x)/(1+e^(x)) . Also find the point of inflection.