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|29 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)

Determine all the critical points for the function : f(x)=xe^(x^2)

Determine all the critical points for the function f(x)=6x^(5)+33x^(4)-30x^(3)+100

The number of critical points of the function f(x)=|x-1||x-2| is

Find the critical points of f(x)=x^(2//3)(2x-1)

Find the critical points of f(x)=x^(3//5)(4-x) .

Find the number of critical points of the function f(x) = |x - 2| + |x +1 | , x in R

Number of critical point of the function f(X) =x+ sqrt(|x|) is _______.