Definite IntegrationHard
Question
If 
= x cos πx, then f′(9)
= x cos πx, then f′(9)Options
A.is equal to -1/9
B.is equal to -1/3
C.is equal to 1/3
D.is non existent
Solution
On differentiating both sides
[f(x)]2 f′(x) = cosπx - πx sinπx
[f(9)]2 ′(9) = -1 .......(i)
Also
= x cos πx ⇒ 
= x cos πx
[f(9)]3 = - 27 ⇒ f(9) = - 3 ........(ii)
from (i) & (ii)
f′(9) = - 1/9
[f(x)]2 f′(x) = cosπx - πx sinπx
[f(9)]2 ′(9) = -1 .......(i)
Also
= x cos πx ⇒ = x cos πx[f(9)]3 = - 27 ⇒ f(9) = - 3 ........(ii)
from (i) & (ii)
f′(9) = - 1/9
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