1hmmmmmmmm
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~
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)
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2 Answers
1
66We have
f^\prime(10)=\lim_{\Delta x\to 0}\dfrac{f(10+\Delta x)-f(10)}{\Delta x}
Using the given relation, we get
f(10+\Delta x)=f(10)+f(\Delta x)+100\Delta x
Therefore,
\dfrac{f(10+\Delta x)-f(10)}{\Delta x}=\dfrac{f(\Delta x)}{\Delta x}+100
Taking limit, and using the fact that the limit of f(x)/x =0 as x->0, we get f'(10)=100
