Value of function

Suppose that f is differentiable function with property f(x+y)=f(x)+f(y)+x2y and Lt x→0 f(x)/x =0

Find the value of f'(10)

2 Answers

1
°ღ•๓яυΠ·

hmmmmmmmm

puttin y=0 u get f(x) =0

then frm d given limit u get
f'(0)=0

nw diffrntiate d given equation

ie

f(x+y)=f(x)+f(y)+x^2y

n then after diffrntiatiing put y=0

u get
f'(x) =x^2

so f'(10)=100

:D

cheero~

66
kaymant ·

We have
f(10)=limΔx0Δxf(10+Δx)f(10)
Using the given relation, we get
f(10+Δx)=f(10)+f(Δx)+100Δx
Therefore,
Δxf(10+Δx)f(10)=Δxf(Δx)+100
Taking limit, and using the fact that the limit of f(x)/x =0 as x->0, we get f'(10)=100

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