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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 `7a tx=2.` The derivative of the function `f(x)-f(4x)a tx=1` has the value equal to `19` (b) 9 (c) 17 (d) 14

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Let y=f(x)-f(2x)
`y'(1)=f'(1)-f'(2)xx2=5rArrf'(1)-2f'(2)=5. . . . . .(1)`
`y'(2)=f'(2)-2f'(4)=7rArrf'(2)-2(4)=7 . . . . . .(2)`
Given, g(x)=f(x)-f(4x)-16x
`rArr" "g'(x)=f'(x)-4f'(4x)-16`
So, g'(1)=f'(1)-4f'(4)-16
from (1) and (2)
`:." "f'(1)-4f'(4)=19`
`:." "g'(1)19-16=3`
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