Home
Class 12
MATHS
Show that f(x)=x^3-6x^2+24x+4 has neithe...

Show that `f(x)=x^3-6x^2+24x+4` has neither a maximum nor a minimum value.

Text Solution

Verified by Experts

`f(x)=x^3-6x^2+24+4=f(x)=3x^2-12x+24=3(x^2-4x+8)=3((x-2)^2+4)` as `f(x)ne`0 for all `x in R` the function has neither a local maximum nor local minum. But has a absolute minimum 12 at x =2.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    MBD PUBLICATION|Exercise QUESTION BANK|127 Videos
  • TRIGONOMETRIC FUNCTIONS

    MBD PUBLICATION|Exercise QUESTION BANK|267 Videos

Similar Questions

Explore conceptually related problems

Find the maximum and minimum value of x+1/x

Find the points where f(x)=8x^2-x^4-4 has local maximum or minimum.

Find the value of.x for which the function f(x) =x^4 — 4x^3 + 4x^2 - 1 is maximum or minimum.

Show that for f(x) = x+1/x the local maximum is less than local minimum.

Show that f(x)=(logx)/x has minimum value at x=e

Obtain the extreme point of f(x) = e^x (x^2-6x +9) . As certain whether they are maximum or minimum points. Find the extreme values at these points.

Find the point of local maxima and local minima of the function f(x) = sin x - cos x, 0 lt x lt 2pi . Also, find the local maximum and local minimum values.

Find the values of x for which f(x) = x^4+2x^3-2x^2-6x+5 is locally maximum and minimum.

Find the value of X for which f(X) is either a local maximum or a local minimum when f(X) = X^3-3X^2-9X+6 .

For which value of x, the function f(x)=4-x-x^2 is maximum or minimum.