Home
Class 12
MATHS
Find the points at which the function...

Find the points at which the function `f` given by `f(x)=(x-2)^4(x+1)^3` has local maxima and local minima and points of inflexion.

Text Solution

Verified by Experts

f(x)=`x^(2)+(1)x^(2)`
`f(x)=2x-(2)/(x^(3))`
Let f(x) =0 Then `x^(4)=1 pm r x=pm1`
Also f(x) = `2+(6)/(x^(4))gt0 forall xne0`
Thus both the points ,x =1 and x=-1 are the points of minima.
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Solved Examples|20 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercise 6.1|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Find the points at which the function f given by f(x)=(x-2)^4(x+1)^3 has local maxima local minima point of inflexion

Find the points at which the function f given by f (x) = (x-2)^(4)(x+1)^(3) has (i) local maxima (ii) local minima (iii) point of inflexion

Find the points at which the function f given by f(x)=(x-5)^4 has local minima and find the local minimum value.

Find the points at which the function f given by f(x)=(x+1)^3 has local minima and find local minimum value.

Find the points at which the function f given by f(x)=x^3-3x has local minima and local maxima.

Show that the function f(x)=4x^3-18x^2+27x-7 has neither local maxima and local minima

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

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

Find the intervals in which the function f given by f(x) = 2x^(2) – 3x is (a) increasing (b) decreasing

Find the intervals in which the function f given by f(x) = x^(2) – 4x + 6 is (a) increasing (b) decreasing