Problem verification

CleMatt

New member
Joined
Jan 13, 2020
Messages
4
Hello, I would like some help verifying i have the correct answers to make sure im on the right track. Any help would be greatly appreciated :) thank you!
 

Attachments

HallsofIvy

Elite Member
Joined
Jan 27, 2012
Messages
5,544
We can't "verify" your answers without seeing what your answers are! You appear to have forgotten to post your answers.
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
5,886
Let's at least make the problem easier to see:

FMH119925 question.png

Please show us your work as far as you got, in addition to your actual answers; and tell us what you are unsure of.
 

HallsofIvy

Elite Member
Joined
Jan 27, 2012
Messages
5,544
\(\displaystyle s(t)= 3t^2- t^3= t^2(3- t)\). \(\displaystyle t^2\) is non-negative for all t and 0 only for t= 0, 3- t= -(t- 3) is positive for t< 3, 0 at t= 3, and negative or t>3. So for t< 0, s(t) is the product of two positive numbers so is positive. s(t)= 0. s(t) is the product of two positive number so is positive again for 0< t< 3. s(3)= 0. s(t) is the product of positive and a negative so is negative for t> 3.

So, the graph, as we go from negative to positive, comes down from the top left corner of the graph ("from infinity) to (0, 0) where it is tangent to the s-axis, goes back up to some maximum value, then back down to (3, 0) and then down to the lower right corner of the graph (to negative infinity.

Do you understand that the velocity function and acceleration function are the first and second derivatives of \(\displaystyle s(t)= 3t^2- t^3\)? Do you know what those derivatives are?
 

CleMatt

New member
Joined
Jan 13, 2020
Messages
4
This was how i approached the problem, i just don't think i am on the right track, so any reviews and feedback would be great!
 

Attachments

CleMatt

New member
Joined
Jan 13, 2020
Messages
4
This was how i approached the problem, i just don't think i am on the right track, so any reviews and feedback would be great!
okay, i think i have just noticed my data entry on my calculator has completely thrown me for my graphs
 

CleMatt

New member
Joined
Jan 13, 2020
Messages
4
1578997939131.png1578998151510.png
I believe these graphs are an actual representation of the data.

Although for the third question, are they asking to supply the answers for both graphs, or to get one single answer from utilizing both graphs?
 

HallsofIvy

Elite Member
Joined
Jan 27, 2012
Messages
5,544
It is impossible to tell what they are asking for because you have not told us what the question is! Apparently you are given the function s(t)= 3t^2- t^3 and are asked to graph it and its derivative, s'(t)= 6t- 3t^2. Is that right? If so then the graphs in your second post are correct.

For III you calculate the derivative of \(\displaystyle f(x)= 3x^2\) at x= 2 using the limit of the difference quotient. Is that what the problem asked you to do? Yes, that derivative is 6(2)= 12.
 
Top