Question

use f(x)=2x^2 to evaluate f(x+h)-f(x)/h

Answer 1

lets take it step by step, although in a week you will be able to do this in your head

Answer 2

k

Answer 3

\(f(x)=2x^2\), so \(f(x+h)=2(x+h)^2\) and now some (careful) algebra

Answer 4

\[f(x+h)=2(x+h)^2=2(x+h)(x+h)=2\left(x^2+2xh+h^2\right)\]
\[=2x^2+4xh+2h^2\]

Answer 5

so far so good?

Answer 6

yes

Answer 7

now it is easy from here on in because
\[f(x+h)-f(x)=2x^2+4xh+2h^2-2x^2=4xh+2h^2\] as \(2x^2-2x^2=0\)

Answer 8

finally divide by \(h\)
since each term has an \(h\) in it, they will cancel as follows
\[\frac{f(x+h)-f(x)}{h}=\frac{4xh+2h^2}{h}=\frac{h(4x+2h)}{h}=4x+2h\]

Answer 9

all details are there, hope it is clear

Answer 10

yes! Thank you.