mt165s2010_2

mt165s2010_2 - Page 3 4 A ladder 3 meters long with one end...

This preview shows pages 1–4. Sign up to view the full content.

Math 165 Midterm Exam Part II Spring 2010 Full Name: TA: Section: Instructions: Show all work. No credit allowed for mere answers with no work shown. Show the steps of calculations. State the reasons that justify conclusions. Give exact values in results. Questions 1, 2, 3 are each worth 12 points. Questions 4, 5 are each worth 15 points. 1. Find the equation of the tangent line to y = 1 x 2 + 4 at the point ± 2 , 1 8 ² .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Math 165 Midterm Part II Page 2 2. Sketch the graph of a function g ( x ) that satisﬁes the following conditions. Be sure to label your graph. (a) g ( x ) is continuous at x = 1 (b) g 0 (1) does not exist (c) g (1) = g (2) = 3 (d) lim x 2 + g ( x ) = -∞ (e) lim x →∞ g ( x ) = 1 3. Identify all critical points and ﬁnd the maximum and minimum value of the function f ( x ) = x 3 - 3 x 2 + 1 on S = [ - 1 , 4].
Math 165 Midterm Part II

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Page 3 4. A ladder 3 meters long, with one end on the ground, is raised so that the angle θ of the ladder with the ground increases by 2 . 5 radians per minute. Consider the right triangle formed by the ladder, the ground, and a vertical line through the top of the ladder. How fast is the area of this triangle increasing at the time when the angle θ equals π/ 6? Math 165 Midterm Part II Page 4 5. Consider the function f ( x ) = x 4-4 x 3-10. (a) Find the intervals on which f is increasing and the intervals on which f is decreasing. (b) Find the intervals on which f is concave up and the intervals on which f is concave down. (c) Find all inﬂection points of f ....
View Full Document

{[ snackBarMessage ]}

Page1 / 4

mt165s2010_2 - Page 3 4 A ladder 3 meters long with one end...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online