Question

Given: F(x) = x^2, find [F(x+h)-F(x)]/h and simplify.

When I did it this is how I attempted to solve it....
[F(x) + F(h) -F(x)]/h
the F(x)'s cancel..
F(h)/h
The closest answer to that was just plain h, so I chose that. But it is incorrect. Can someone walk me through the process? Thanks :)

Answer 1

Hmm... the F(x) just can't cancel... but don't worry! You'd get it right in a minute!

Answer 2

u cannot write f(x+h) as f(x)+f(h) ...!!

Answer 3

\[F(x)=x^2 \implies F(\text{some number}) = \text{that number}^2 \]

Answer 4

\[F(x) = x^2\implies F(x + h) = (x + h)^2 \]Do you agree?

Answer 5

Hmm. Wouldn't it be F(x^2+h) though? Because only F(x) is x^2. & It doesn't say that h is changed to anything.

Answer 6

That's what a function means, @theequestrian.

Answer 7

Wait, so it is F(x+h)^2 ? Sorry, I'm just confused.. But thanks for helping !

Answer 8

the procedure:
to find f(x+h) , u just replace x in f(x) by (x+h).
remember this.
ok?

Answer 9

Okay, I'm with you

Answer 10

so now replace x with (x+h) in \(x^2\)
what u get??

Answer 11

(x+h)^2

Answer 12

thats your f(x+h) ok?
so f(x+h)-f(x)=(x+h)^2-x^2
ok?

Answer 13

Okay, then (x+h) simplifies to x^2+2xh+h^2 right?

Answer 14

yup,
so whats
x^2+2xh+h^2-x^2 ?

Answer 15

2xh+h^2

Answer 16

great :)
now the question was [F(x+h)-F(x)]/h
u got numerator as 2xh+h^2
so whats
(2xh+h^2)/h = ?

Answer 17

2x+h ?

Answer 18

thats your final answer.. good work :)

Answer 19

One question. I thought you couldn't reduce with addition or subtraction in the fraction?

Answer 20

i did not understand your question...can u give example?

Answer 21

Like in (2xh+h^2)/h there is addition in the numerator. I thought you could not cancel out anything from the bottom if there was addition or subtraction (addition in this case) in the numerator ? Does that make more sense?

Answer 22

\[\frac{2xh+h^2}{h}=\frac{h(2x+h)}{h}=2x+h\]
ok?

Answer 23

Ohhh. I see now! Thanks for clarifying :)

Answer 24

welcome :)