f'x=ϕx and ϕ'x=fx for all x. Also f3=5 and f'3=4. Then the value of f102-ϕ102 is _____

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answer is 9.

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Detailed Solution

ddxfx2-ϕx2 =fx.f'x-ϕx-ϕ'x =2fx.ϕx-ϕx.fx f'x=ϕx and ϕ'x=fx =0or fx2-ϕ102= constant∴ f102-ϕx2=f32-ϕ32=f32-f'32 =25-16=9

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