Question

If g(t)=4t-t^2, find g(t+h)-g(t)/h. Can someone please tell or show me step by step how to do this problem. I am having a hard time starting it

Answer 1

You got \[g(t)=4t-t^2\]
If you have g(t+h), that means everytime you see "t" substitute (t+h).
\[g(t+h)=4(t+h)-(t+h)^2\]

Answer 2

\[\large\dfrac{g(t)}{h}=\dfrac{4t-t^2}{h}\]

Answer 3

ok. I'm looking over it. I am trying to make sure I understand it. Thanks so much for your quick reply

Answer 4

@aebiri2 You can just substitute what I just told you into what they want you to give.

Answer 5

Ok, thanks. Doing that right now

Answer 6

@Azteck I am still having trouble solving it. I guess I don't know how to go about simplifying it to get the correct answer. This is what I have so far (4t+4h)-(t^2+2th+h^2)-(4t-t^2)/h

Answer 7

why are there three terms?

Answer 8

I guess when I substituted for g(t+h) I created two terms via that route alone

Answer 9

so 4(t+h)-(t+h)^2

Answer 10

Oh yeah sorry about that. I'm on three windows at the moment. Yeah you're correct.

Answer 11

Start by combining the fraction with (4t+h)

Answer 12

\[(4t+h)-\frac{ 4t-t^2 }{ h }=\frac{ h(4t+h)-(4t-t^2) }{ h }\]

Answer 13

@aebiri2

Answer 14

You would get 4h^2-t^2h simplified right?

Answer 15

On the numerator?

Answer 16

or the whole shibang?

Answer 17

yes. There wouldn't be anything on the denominator because you multiplied the h to get rid of it

Answer 18

just on what you had typed

Answer 19

prior

Answer 20

That's incorrect.

Answer 21

Should I multiply the h through out the whole numerator so h (4t+4h)-(t^2+2ht+h^2)-(4t-t^2)

Answer 22

\[4(t+h)-(t+h)^2-\frac{ 4t-t^2 }{ h }=(t+h)[4-(t+h)]-\frac{ 4t-t^2 }{ h }\]

Answer 23

\[=\frac{ h(t+h)[4-(t+h)]-(4t-t^2) }{ h }\]

Answer 24

\[=\frac{ (ht+h^2)[4-(t+h)]-4t+t^2 }{ h }\]
\[=\frac{ 4ht-ht(t+h)+4h^2-h^2(t+h)-4t+t^2 }{ h }\]

Answer 25

\[=\frac{ 4ht-ht^2-h^2t+4h^2-h^2t-h^3-4t+t^2 }{ h }\]
\[\frac{ 4ht-ht^2-2h^2t+4h^2-h^3-4t+t^2 }{ h }\]

Answer 26

@aebiri2 Do you have the correct answer on an answer sheet?

Answer 27

The correct answer is 4-2t-h. Sorry I was trying to figure out what you did

Answer 28

Is the question asking you for this:
\[\frac{ g(t+h)-g(t) }{ h }\]
or this:
\[g(t+h)-\frac{ g(t) }{ h }\]

Answer 29

I bet it's the first one @aebiri2

Answer 30

\[\frac{ 4(t+h)-(t+h)^2-(4t-t^2) }{ h }=\frac{ 4t+4h-t^2-2th-h^2-4t+t^2 }{ h }\]
Please use brackets when writing down an equation. You kind of confused me because I though it was the second one.

Answer 31

\[=\frac{ 4h-2th-h^2 }{ h }\]
\[=4-2t-h\]

Answer 32

@aebiri2 look at this now.

Answer 33

It was asking for the first one. I am reviewing it now

Answer 34

Sorry for the confusion

Answer 35

@Azteck Thank you so so so much. I got it. whew

Answer 36

no worries