DifferentiationHard
Question
If 8 f(x) + 6 f 
= x + 5 and y = x2 f(x), then 
at x = -1 is equal to
= x + 5 and y = x2 f(x), then at x = -1 is equal to Options
A.0
B.1/14
C.-1/14
D.None of these
Solution
8 f(x) + 6 f 
= x + 5 .... (i)
Replacing x by 1/x we get
8 f
+ 6 f(x) = 1/x + 5 .... (ii)
(i) × 8 ⇒ 64 f(x) + 48 f
= 8x + 40 .... (iii)
(ii) × 6 ⇒ 36 f(x) + 48 f
+ 30 ..... (iv)
(iii) - (iv) ⇒ 28 f(x) = 8x -
+ 10
Differentiating w.r.t. x
28 f′(x) = 8 +
Now y = x2 f(x)
⇒
= x2 f′(x) + 2x f(x)
⇒
= f′(- 1) - 2f(- 1)
=
- 2 (2/7) = 
{∵ f(-1) = 2/7}
= x + 5 .... (i)Replacing x by 1/x we get
8 f
+ 6 f(x) = 1/x + 5 .... (ii)(i) × 8 ⇒ 64 f(x) + 48 f
= 8x + 40 .... (iii)(ii) × 6 ⇒ 36 f(x) + 48 f
+ 30 ..... (iv)(iii) - (iv) ⇒ 28 f(x) = 8x -
+ 10Differentiating w.r.t. x
28 f′(x) = 8 +
Now y = x2 f(x)
⇒
= x2 f′(x) + 2x f(x)⇒
= f′(- 1) - 2f(- 1)=
- 2 (2/7) = {∵ f(-1) = 2/7}Create a free account to view solution
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