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
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B
9
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C
17
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D
14
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Solution
The correct option is A19 The derivative will be,f′(x)−2f′(2x) f′(x)−2f′(2x)|1=5=f′(1)−2f′(2)...........(1) f′(x)−2f′(2x)|2=7=f′(2)−2f′(4) Hence, 14=2f′(2)−4f′(4) ........................(2) Adding (1) and (2), 19=2f′(2)−4f′(4)+f′(1)−2f′(2) ⇒f′(1)−4f′(4)=19