CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

At which of the following points does f(x)=x4  has a maximum?


  1. 0

  2. 1

  3. 2

  4. 3

  5. None of these


Solution

The correct option is E

None of these


We saw that the necessary condition for f(x) to have a maximum at x=cisf(c)=0

We have f(x)=4x3

f(x)=0x=0. Now we have to check if x=0 is a local maxima. For that, we have to check with nth derivative test conditions -

If  f(x) has derivative upto nth order and f(c)=f(c)..fn1(c)=0, then

A)    n is even, fn(c)<0x=c is a point of maximum

B)     n is even, fn(c)>0x=c is a point of minimum

C)    n is odd, fn(c)<0f(x) is decreasing about x=c

D)    n is odd, fn(c)>0f(x) is increasing about x=c

So, we will differentiate the given function until we get a non negative value at  x=0

f(x)=x4

f(x)=4x3

f(x)=12x2

f(0)=0

f(x)=f3(x)=24x

f3(0)=0

f(x)=f4(x)=24

f4(x)=24

 n is even, fn(c)>0x=c is a point of minimum

x=0 is a local minimum. So this function does not have any local maximum.

flag
 Suggest corrections
thumbs-up
 
0 Upvotes



footer-image