sample_midterm2

sample_midterm2 - Math 016A Name ID Midterm 2 Signature Mar...

This preview shows pages 1–3. Sign up to view the full content.

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: Math 016A Name: ID Midterm 2 Signature Mar., 2009 Simplify your ﬁnal result if possible. No Calculators allowed. 1. (20pts)[a](8pt) Find the derivative of f (x) = [x2 (2x + 3)]3 . [b](12pt) Find the second derivative and solve the equation f (x) = 0 for f (x) = x x2 +1 2. (16pts) Find the equation of the tangent line to the graph of the following curve at point ( π , 1 ) : 22 √ sin x + 2 cos(xy ) = 1 + 2 1 3. (14pts) A boat is pulled by a winch on a dock and the winch is 8 feet above the deck of boat. The winch pulls the rope at the rate of 3f t/s. Find the speed of the boat when 10 feet of rope is out. What happens to the speed of the boat as it gets closer and closer to the dock? 4. (16pts)Find the critical numbers and open intervals on which the function f (x) = √ −3x 2x + 1 is increasing or decreasing. 2 5. (17pts)Find and identify all the local extrema of f (x) = x + 1 . x−1 6. (17pts)Find the global extrema of the function f (x) = 2 cos x − sin(2x) on the interval [0, 2π ]. Note that you may want to use trigonometric identities: sin(2θ) = 2 sin θ cos θ, or cos(2θ) = 2 cos2 θ − 1 = 1 − 2 sin2 θ. 3 ...
View Full Document

{[ snackBarMessage ]}

Page1 / 3

sample_midterm2 - Math 016A Name ID Midterm 2 Signature Mar...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online