Question #21f32

1 Answer
Dharma R.
Sep 17, 2015

f(x+h)= (2(x+h)-1)/(x+h+3)
f(x) = (2x-1)/(x+3
f(x+h)-f(x)= (2(x+h)-1)/(x+h+3)-(2x-1)/(x+3
numerator is
2x^2+2(h+3)x+6h-x-3-(2x^2+2hx+6x-x-h-3)
=7h
demonimator
(x+h+3)*(x+3)
f'(x)=Lt_h->0(f(x+h)-f(x))/h
so Lt_h->_0 (7h)/((x+h+3)h(x+3)
cancelling h and applying Ltgives
7/(x+3)^2
=>f'(x)=7/(x+3)^2
f'(3)=7/36

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