Question

f(x+h)-f(x)/h
f(x)=2x^2-5x

how does this H play in??

Answer 1

@jim_thompson5910

Answer 2

let's find what f(x+h) is equal to

start with f(x)=2x^2-5x

then replace every copy of x with (x+h)

so we'll then have f(x+h)=2(x+h)^2-5(x+h)

making sense so far?

Answer 3

wait. so f(x+h)-2(x+h)^2-5(x+h)/h, ok yes that makes sense.

Answer 4

we're focusing on just f(x+h) for now. Don't worry about [f(x+h)-f(x)]/h

Answer 5

Do you see how I went from
f(x)=2x^2-5x
to
f(x+h)=2(x+h)^2-5(x+h)
??

Answer 6

ohh, you even replaced the f(x) with x+h, too. Yes i do see where you're coming from

Answer 7

yes every x gets replaced with x+h even the first x

so we go from f(x) to f(x+h)

Answer 8

yes yes

Answer 9

now let's simplify the right side of f(x+h)=2(x+h)^2-5(x+h)

Answer 10

how would you simplify 2(x+h)^2-5(x+h) ?

Answer 11

or I guess I should say "expand out"

Answer 12

oh ok, so we're multiplying 2 by (x+h)^2 and -5 by (x+h)

Answer 13

what happens when you FOIL out (x+h)^2 ?

Answer 14

x^2+xh+xh+h^2

Answer 15

which becomes x^2+2xh+h^2

Answer 16

okay now multiply all those terms by 2?

Answer 17

\[\Large f(x+h) = 2(x+h)^2-5(x+h)\]
\[\Large f(x+h) = 2(x^2+2xh+h^2)-5(x+h)\]
now distribute