Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 12-science Answered

 I want to ask  the quation that the second derivative test for maxima and minima as f ?(c)=0 then tangent is parallel to x axis at the point x=c .then how can we take double derivative at x=c that is f ??(c).>0 same thing about minima.

Asked by Kalyanrao Chavan | 22 Aug, 2014, 10:18: PM
answered-by-expert Expert Answer
For space straight f apostrophe apostrophe left parenthesis straight c right parenthesis comma space straight f apostrophe left parenthesis straight c right parenthesis equals 0 Suppose space 0 less than straight f apostrophe apostrophe left parenthesis straight c right parenthesis rightwards double arrow 0 less than limit as straight h rightwards arrow 0 of fraction numerator straight f apostrophe left parenthesis straight c plus straight h right parenthesis minus straight f apostrophe left parenthesis straight c right parenthesis over denominator straight h end fraction rightwards double arrow 0 less than limit as straight h rightwards arrow 0 of fraction numerator straight f apostrophe left parenthesis straight c plus straight h right parenthesis minus 0 over denominator straight h end fraction rightwards double arrow limit as straight h rightwards arrow 0 of fraction numerator straight f apostrophe left parenthesis straight c plus straight h right parenthesis over denominator straight h end fraction greater than 0 Thus space for space straight h space sufficiently space small comma space fraction numerator straight f apostrophe left parenthesis straight c plus straight h right parenthesis over denominator straight h end fraction greater than 0 straight f apostrophe left parenthesis straight c plus straight h right parenthesis less than 0 comma space for space straight h less than 0 space left parenthesis straight f space is space decreasing space as space it space is space decreasing space from space the space left space from space straight x right parenthesis straight f apostrophe left parenthesis straight c plus straight h right parenthesis greater than 0 comma space for space straight h greater than 0 space left parenthesis straight f space is space increasing space as space it space space is space increasing space from space the space right space from space straight x right parenthesis By space first space derivative space test comma space straight f left parenthesis straight x right parenthesis space has space local space minimum space at space straight c.
Answered by Prasenjit Paul | 25 Aug, 2014, 11:30: AM

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 12-science - Maths
x=acos^3theta and y=bsin^3theta find d^2y/dx^2.
Asked by gunturiabhishek | 18 Oct, 2020, 03:40: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
if x=a(1-cosθ ),y =b sinθ , then find dy/dx and d^2y/dx^2.
Asked by Gothai | 28 Aug, 2018, 11:33: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
If x = a cos thita + b sin thita and y = a sin thita – b cos thita, show that y2d2y/dx2 – x dy/dx + y = 0 explain in great detail
Asked by haroonrashidgkp | 25 Aug, 2018, 07:15: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
If x = a(cos thita + thita sin thita) and y = a(sin thita – thita cos thita), show that d2y/dx2 = 1/a (sec3thita / thita) Explain in great detail
Asked by haroonrashidgkp | 25 Aug, 2018, 07:15: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
If y = {x + (x2 + 1)1/2}m then show that (x2 + 1)d2y/dx2 + x dy/dx – m2y = 0
Asked by haroonrashidgkp | 25 Aug, 2018, 07:13: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
If y = ea cos-1 x  , -1 <_  x _< 1 show that (1 – x2)d2y/dx2 – x dy/dx – a2y = 0       explain in great detail
Asked by haroonrashidgkp | 25 Aug, 2018, 07:05: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Find the second order derivative of  sin 3x cos 5x  
Asked by haroonrashidgkp | 24 Aug, 2018, 11:12: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Find the second order derivative  of e3x sin 4x Explain in great detail  
Asked by haroonrashidgkp | 24 Aug, 2018, 11:12: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
If y = sec x – tan x , show that  (cos x)d2y/dx2 = y2 Explain in great detail
Asked by haroonrashidgkp | 24 Aug, 2018, 11:11: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Differentiate space straight y equals square root of fraction numerator straight x squared plus 2 over denominator straight x squared plus 3 end fraction end root 
Asked by Topperlearning User | 01 Aug, 2014, 01:27: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×