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Hi there, I just started calculus and I'm having trouble with these particular questions, my teacher has a hard time teaching and doesn't really care about online students, so it has been really hard teaching myself.

https://ibb.co/8NjLbkP
https://ibb.co/5R10Xxd
https://ibb.co/yFpVFwV
https://ibb.co/W3JN2KH The second question for this picture
https://ibb.co/WcNHXYs
https://ibb.co/2Nq5YjZ
https://ibb.co/MBPdmCw

Hi s.h_math (https://biology-forums.com/index.php?action=profile;u=1067569),

Do you mind copy/pasting the text of the question instead of linking the images? The questions are easier to reference when answering. Or you can upload the pictures to our website, and it automatically converts them to text.


I am assuming he wants you to graph these equations on an x-y plane and then create a tangent line from it.

Did your teacher teach the definition of a derivative yet? That is: f(x) = [ f(x+h) - f(x) ] / h ?

Here's what (a) should look like:

(https://biology-forums.com/gallery/44/6_07_02_22_7_26_01.png) (https://biology-forums.com/index.php?action=gallery;sa=view&id=44360)

It looks like the equation of the tangent is: \(y = -2x - 1\)

Here's what (b) should look like:

(https://biology-forums.com/gallery/44/6_07_02_22_7_29_48.png) (https://biology-forums.com/index.php?action=gallery;sa=view&id=44361)

It is because it's saying the image is too short, not sure why because that's what I usually do, sorry sir.

Post Merge: 2 years ago

and yes he did teach that equation

Yeah, that's weird. What's the exact error?

Does the website where you get to see the questions allow you to copy the text?

5) A company that sells sweatshirts finds that the profit can be modelled by \(P(s) =-0.30s^2 + 3.5s + 11.15\) where P(s) is the profit. in thousands of dollars, and s is the number of sweatshirts sold (expressed in thousands).

For this question, you have to repeat these steps for ii, iii, and iv

(https://biology-forums.com/gallery/44/6_07_02_22_7_46_32.png) (https://biology-forums.com/index.php?action=gallery;sa=view&id=44362)


Example 2: A rock is tossed upward from a diff that is 120 meters the water The height of rock —5t2 + tot + 120. where h is above the water is modelled by h(t) seconds. Calculate the average rate of change in height during each time intervals.

(https://biology-forums.com/gallery/44/6_07_02_22_8_47_31.png) (https://biology-forums.com/index.php?action=gallery;sa=view&id=44363)


(https://biology-forums.com/gallery/44/6_07_02_22_9_13_55.png) (https://biology-forums.com/index.php?action=gallery;sa=view&id=44364)

THANK YOU SO MUCH FOR HELPING ME LEARN, ITS REALLY BEEN HARD FOR ME BECAUSE OF MY TEACHER. ONLINE SCHOOL ISN'T THE BEST FOR TEACHERS BECAUSE I GUESS ITS HARD FOR THEM TO FOCUS ON ONLINE STUDENTS. HOWEVER, THE TEACHER DOESN'T EVEN TRY. SO, THNK YOU ONCE AGAIN FOR ALWAYS BEING A GREAT HELP FOR ME :).

I made a nasty error here.

I divided by 2, but I should have divided by one because the interval is between 0 and 1, so 1 minus 0.

Apologies for that.

Oh no problem, for average correct?

Post Merge: 2 years ago

For the next question I would also divide by one correct?

For that same link, right? Yes, between 1 and 2 would mean you divide by 1 also because 2 - 1 is 1.

Does that make sense?

yes for sure, Thank you!

Post Merge: 2 years ago

sir for the first question, the teacher wants us to use the equation he wrote where you used a graph.

The one that looks like \(m=\frac{f\left(x+h\right)-f\left(x\right)}{h}\) ?

Yes, that's correct!

(https://biology-forums.com/gallery/44/6_08_02_22_10_29_27.png) (https://biology-forums.com/index.php?action=gallery;sa=view&id=44365)

Ok, I did this really quickly because I have a class to teach for the next two hours. Review it, see if it makes sense, and I'll reply back as soon as I can.

I understand, but I'm not sure where you got +5 after the +3.

y = x^2 - 6x + 3
y = (2)^2 - 6(2) + 3
y = 4 - 12 + 3 = -5

Once you put that into the formula, two negatives make a positive, hence +5

do you mean where it says -f(x) that's the second neg that makes it positive?

Post Merge: 2 years ago

do you mean where it says -f(x) that's the second neg that makes it positive?

Exactly 👍

oh okay I believe I understand. Thank you. basically, if it was a positive 5, in the equation I would sub in -5, correct?

Technically, yes. We got -5 as the output, then we put it as f(x) in the formula which had a negative at the front, for example

... - f(x)
... - (-5)
... + 5

also sir one last question, where do you get (h-2) from?

You see where we simplified to h^2 - 2h? I common factored an 'h' from it, so:

h(h-2)

Then, given that the denominator had an 'h' also, it cancelled with the factored 'h' above, leaving me with h-2 as my final expression.

Do you see it?

wouldn't it be done like this sir?

Post Merge: 2 years ago

https://ibb.co/RbBndHB

You could do it that way where you don't evaluate f(2) until the very end, as you did in your sample.

What I did was evaluate x right from the beginning -- doesn't matter either way.

Also, I didn't take the limit as h->0. But if I did, I would get the same answer:

\(m = h - 2\)

\(m\ =\ \lim _{h\ \rightarrow 0}\left(h-2\right)\)

\(m\ =\ -2\)

Thank you so much for all your help!