Asked by Anonymous
simplify (f(x+h)-f(h))/h where f(x)=2x^2+x.
Answers
Answered by
Reiny
f(x)=2x^2+x
f(x+h) = 2(x+h)^2 + x+h
= 2x^2 + 4hx + 2h^2 + x + h
then (f(x+h)-f(h))/h
= (2x^2 + 4hx + 2h^2 + x + h - (2x^2+x) )/h
= (4hx + 2h^2 + h)/h
= h(4x + 2h + 1)/h
= 4x + 2h + 1 , h ≠ 0
In your next step you will be expected to take the limit of that
expression as h ---> 0
and leading up to derivatives. Fun times ahead! Enjoy the mathemagics.
f(x+h) = 2(x+h)^2 + x+h
= 2x^2 + 4hx + 2h^2 + x + h
then (f(x+h)-f(h))/h
= (2x^2 + 4hx + 2h^2 + x + h - (2x^2+x) )/h
= (4hx + 2h^2 + h)/h
= h(4x + 2h + 1)/h
= 4x + 2h + 1 , h ≠ 0
In your next step you will be expected to take the limit of that
expression as h ---> 0
and leading up to derivatives. Fun times ahead! Enjoy the mathemagics.
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