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Suppose the function f(x)-f(2x) has the ...

Suppose the function f(x)-f(2x) has the derivative 5 at x=1 and derivative 7 at x= 2. The derivative of the function f(x)-f(4x) at x=1 has the value equal to

A

19

B

9

C

17

D

14

Text Solution

Verified by Experts

`y=f(x)-f(2x) or y'=f'(x)-2f'(2x)`
`"or "y'(1)=f'(1)-2f'(2)=5, and " (1)"`
`y'(2)=f'(2)-2f'(4)=7" (2)"`
Now, let `y=f(x)-f(4x)`
`therefore" "y'=f'(x)-4f'(4x)`
`"or "y'(1)=f'(1)-4f'(4)" (3)"`
Substituting the value of `f'(2)=7+2f'(4) in (1),` we get
`f'(1)-2(7+2f'(4))=5`
`f'(1)-4f'(4)=19`
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