Home
Class 12
MATHS
The function f(x)=x^(5)-5x^(4)+5x^(3) fi...

The function `f(x)=x^(5)-5x^(4)+5x^(3)` find maximum and minimum value

A

One minima and two maxima

B

Two minima and one maxima

C

Two minima and two maxima

D

One minima and one maxima

Text Solution

Verified by Experts

The correct Answer is:
D
`f'(x)=5x^(4)-20x^(3)+15x^(2))`
`f''(x)=20x^(3)-60x^(2)+30x`
`f'(x)=0 rArr x^(2)(x^(2)-4x+3)=0`
`rArr" "x^(2)(x-1)(x-3)=0 rArr x=0, 1, 3`
`f''(1)lt0 and f''(3)=540-540+90 gt0`
`and f''(0)=0 and f'''(0) ne0`
`therefore" Maximum at x = 1 and minimum at x = 3"`
Promotional Banner

Topper's Solved these Questions

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|10 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Comprehension Type|6 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Linked comprehension Type|2 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Numberical Value Type|5 Videos

Similar Questions

Explore conceptually related problems

The function f(x)=sum_(k=1)^5 (x-K)^2 assumes then minimum value of x given by (a) 5 (b) 5/2 (c) 3 (d) 2

Prove that the function f(x) =kx(x^(2)+a^(2))^(-(5)/(2)) has a maximum value at x=(a)/(2) .

If f(x)=x^5-5x^4+5x^3-10 has local maximum and minimum at x=p and x=q , respectively, then (p , q)= (a) (0,1) (b) (1,3) (c) (1,0) (d) none of these

Show that the function f(x)=(2)/(3)x^(3)-6x^(2)+20x-5 has neither a maximum nor a minimum value.

Show that the function f(x) = 2/3 x^3-6x^2+20x-5 has neither a maximum nor a minimum value.

Show that, f(x) =sinx-(x^(3))/(3!)-(x^(5))/(5!) is neither maximum nor minimum at x=0.

If the function y=f(x) is represented as x=phi(t)=t^5-5t^3-20 t+7 , y=psi(t)=4t^3-3t^2-18 t+3(|t|<2), then find the maximum and minimum values of y=f(x)dot

Show that the function 2x^(3)+3x^(2)-36x+10 has a maximum value at x=-3 and a minimum value at x=2 , also find the maximum and minimum values of the function.

Find the range of values of x for which the function f(x)=2x^(3)-9x^(2)-24 x+5 increases with x

Show that , the following functions have neither a maximum nor a minimum value : x^(3)-3x^(2)+9x-5