Question

F(x)=x^2-3x find (F(x+h)-F(x))/h

Answer 1

the difference quotient beloved by math teachers

Answer 2

f(x+h) = (x+h)^2 -3(x +h) = x^2 +2xh +h^2 -3x -3h
f(x) = x^2 - 3x
f(x+h) - f(x) = x^2 +2xh +h^2 -3x -3h -x^2 +3x = h^2 - 3h
(F(x+h)-F(x))/h = (h^2 -3h)/ h = h(h-3) / h = h-3

Answer 3

only hard part is figuring out what
\[f(x+h)\] means in this case it is
\[f(x+h)=(x+h)^2-3(x+h)\]
\[=x^2+2xh+h^2-3x-3x\]

Answer 4

typo
\[=x^2+2xh+h^2-3x-3h\]
so
\[f(x+h)-f(x)=x^2+2xh+h^2-3x-3h-(x^2-3x\]
\[=x^2+2xh+h^2-3x-3h-x^2+3x\]
\[=2xh+h^2-3x\]

Answer 5

another typo
\[=2xh+h^2-3h\]

Answer 6

as usual everything without an h in it has gone. so finally
\[\frac{f(x+h)-f(x)}{h}=\frac{2xh-3h+h^2}{h}=\frac{h(2x-3+h)}{h}=2x-3+h\]

Answer 7

Thank you!