Madeline M.

Undergraduate at Vanderbilt, Tutor for 6 years

Tutor Satisfaction Guarantee

Calculus

TutorMe

Question:

Find the maximum and minimum values of the function f(x) = x^3 - 7x^2 + 8x - 1 on the interval [0, 6].

Madeline M.

Answer:

We'll begin by using the first derivative of the function to find any local maxima and minima in the interval. The critical points where maxima and minima may exist are found either where the function is discontinuous or where the first derivative is equal to 0. The function is a polynomial, so it is not discontinuous anywhere over the real numbers. This leaves us with critical numbers found from the first derivative: f'(x) = 3x^2 - 14x + 8 0 = 3x^2 - 14x + 8 0 = (3x - 2)(x - 4) Critical points are found where x = 2/3 and where x = 4 By finding the values of the functions at these points, as well as at the endpoints of the interval, we can find the maximum and minimum values in this interval: f(2/3) = 41/27 or approximately 1.52 f(4) = -17 f(0) = -1 f(6) = 11 The minimum value is -17, found at one of the critical points, while the maximum value is 11, found at the endpoint where x = 6.

ACT

TutorMe

Question:

Choose the option that best replaces the bracketed portion of the sentence. Both City Hall and Holtzmann Tower, the tallest building downtown, [was rebuilt] following the earthquake. A) no change B) were rebuilt C) rebuilt D) had been rebuilt

Madeline M.

Answer:

The correct choice is B, The subject is compound since it includes both City Hall and the Holtmann Tower. The verb must agree with the subject, and therefore should be plural. The verbs for choices A and D are both singular. The verb for choice C is active, which would imply the buildings did the rebuilding themselves.

Algebra

TutorMe

Question:

Find the x- and y-intercepts of the following line: 3x - 2y = 8

Madeline M.

Answer:

A line has x- and y-intercepts where it crosses the x- and y-axes, respectively. Any point on the x-axis will always have a y coordinate of 0, so we can find the x-intercept by substituting 0 for y in the line: 3x - 2y = 8 --> 3x - 2(0) = 8 3x = 8 x = 8/3 So the x-intercept is (8/3, 0). The same process can be applied to finding the y-intercept, this time substituting 0 for x: 3x - 2y = 8 --> 3(0) - 2y = 8 -2y = 8 y = -4 y-intercept: (0, -4)

Send a message explaining your

needs and Madeline will reply soon.

needs and Madeline will reply soon.

Contact Madeline

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.