wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The function fx=-1xtet-1t-1t-23t-35dt has a local minimum at x=


A

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

3

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
E

3 and 4

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is D

3


Explanation for correct option:

We will determine the value of x by using the sign scheme rule.

Following are the rules of sign of scheme:

  1. Make all the coefficients of x positive.
  2. Need to factorize all the terms.
  3. Start assigning signs from extreme right looking at the final equation.
  4. If the power of x is odd-alternate sign in next period.
  5. If the power of is even – carry the the same sign in next period.

The given function is,

fx=-1xtet-1t-1t-23t-35dt

For extremal values f'x=0

Now differentiating with respect to x .

We know that,

ddxϕxψxftdt=fψxψ'x-fϕxϕ'x

So,

f'x=ddx-1xtet-1t-1t-23t-35dt

f'x=xex-1x-1x-23x-35×1

x=0,1,2,3...

For local minima f''x>0

f''x=ex-1x-1x-23x-35+xexx-1x-23x-35+xex-1x-23x-35+3xex-1x-1x-22x-35+5xex-1x-1x-23x-34f''0=0f''1>0f''2<0f''3>0

So, local minima at x=1and x=3

Hence, options B and D are correct answer.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Continuity in an Interval
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon