Tiffany C.

Economics Student at Princeton University

Tutor Satisfaction Guarantee

Calculus

TutorMe

Question:

What do the first and second derivatives tell you about a graph's shape?

Tiffany C.

Answer:

If the first derivative is positive, then that means that the function's value increases with $$x $$, i.e. $$ f(x) > f(x')$$, granted that $$ x > x'$$. If the first derivative is negative, that means that the function's value decreases or appears to be going downhill if you move to the right along the x-axis. The second derivative tells you about the concavity of the function. If the second derivative is positive, its overall shape is concave up, in which it looks like a cup or a U sitting on the x-axis. If the second derivative is negative, it is concave down, in which it looks like an upside down U on the x-axis.

Algebra

TutorMe

Question:

Expand $$(x+4)(x-4)$$.

Tiffany C.

Answer:

Whenever you have a quantity that is in the form $$ (x + a)(x - a)$$, the resulting expansion will always be equal to $$ x^2 - a^2$$. Therefore, the expansion of this equation would be $$ x^2 - 16$$

Physics

TutorMe

Question:

If you were standing on a scale on an elevator, would the scale reading change depend on if the elevator is moving? Why?

Tiffany C.

Answer:

According to Newton's laws, you need a force in order to accelerate a system. Therefore, there must be an imbalance of forces if, in the elevator, you go from resting to moving upwards. If you were accelerating upwards, the normal force of the elevator floor on your body would have to be greater than your actual weight (which is $$mg$$) so that there is a net force going upwards, therefore the scale weight would greater than your actual weight (oh no!).

Send a message explaining your

needs and Tiffany will reply soon.

needs and Tiffany will reply soon.

Contact Tiffany

Ready now? Request a lesson.

Start Session

FAQs

What is a lesson?

A lesson is virtual lesson space on our platform where you and a tutor can communicate.
You'll have the option to communicate using video/audio as well as text chat.
You can also upload documents, edit papers in real time and use our cutting-edge virtual whiteboard.

How do I begin a lesson?

If the tutor is currently online, you can click the "Start Session" button above.
If they are offline, you can always send them a message to schedule a lesson.

Who are TutorMe tutors?

Many of our tutors are current college students or recent graduates of top-tier universities
like MIT, Harvard and USC.
TutorMe has thousands of top-quality tutors available to work with you.