Question

If f(x)=x^2+3x+5 what is f(3+h) ?

Answer 1

substitute 3+h everywhere you have x in the function

Answer 2

\[\Large\bf f(\color{royalblue}{x})=(\color{royalblue}{x})^2+3(\color{royalblue}{x})+5\]
\[\Large\bf f(\color{royalblue}{x+h})=(\color{royalblue}{x+h})^2+3(\color{royalblue}{x+h})+5\]

Do you need this for the difference quotient or something? :o
You'll need to expand everything out if so.

Answer 3

I dont know im so lost D;

Answer 4

You're here, found you.

Answer 5

The mathematical statement f(x) simply means "a function evaluated at x".
Then f(3+h) means "evaluate the function at (3+h)", or even
"everywhere there is an x in the function, write (3+h) instead"

After you've done that, you can expand if necessary; depends on the requirements of your course or if you plan on doing other things with the function after you substitute

Answer 6

Calculating f(3+h) is usually one of the steps in finding the derivative of the function at f(x) at x=3, i.e. f'(3). You would divide by h and let limit h approach zero. This is the definition of derivative..

Answer 7

lol i put x+h :D sorry bout that. misready the question.

Answer 8

It's still the correct method

Answer 9

A. h^2=h=23
B.(x^2+3x+5)
C.(3+h)^2+8+h
D.h^2+9h+23

those were the answer possibilities ??

Answer 10

@Karina_08 Suppose you have some function that's f(elephants)=(elephants)^2+7. Then if I ask you to find f(gorillas and chimps) then you find everywhere elephants were before and replace it and say (gorillas and chimps)^2+7 must be f(gorillas and chimps).

Answer 11

Normally we use x, but it doesn't matter what we put there, it's just a placeholder meaning we can exchange everything with whatever we used to have after the f in parenthesis f(_) and put whatever's there in place of that.

Answer 12

You use this type of calculation, for example, to find the derivative of f(x) :
$$
f'(x)=\cfrac{d}{dx}f(x)=\lim h\to 0\cfrac {f(x+h)-f(x)}{h}\\
$$
So, the derivative of f(x) at x=3 would be:
$$
f'(3)=\cfrac{d}{dx}f(3)=\lim h\to 0\cfrac {f(3+h)-f(3)}{h}\\
$$
So, evaluating f(3+h) would be: \(h^2+9 h+23\), for example.

Answer 13

An h appears and suddenly everyone's got to start talking about how it's arbitrarily used for computing limits in the definition of a derivative in cal 1. lol

Answer 14

I think it unlikely that @Karina_08 is asking her question in a limit context here.

Answer 15

Thanks everyone im obviously not as advanced as you guys but I appreciate the help! ((:

Answer 16

Our pleasure. Don't sell yourself short; education is just a matter of time invested. Given enough, you'll surpass your own expectations.