MATH 20A Study Guide - Final Guide: Maxima And Minima
Name:
PID #:
Section:
MATH 20A
PRACTICE
FINAL
Instructions
• Read each question carefully, and answer each question completely.
• Show all of your work. No credit will be given for unsupported answers.
• Write your solutions clearly and legibly. No credit will be given for
illegible solutions.
# pts
1
2
3
4
5
6
7
8
Σ
1. Evaluate the following derivatives.
(a) (2 points) d
dθ sin(θ)cos(θ)tan(θ)
(b) (2 points) d
dx sin(cos(tan(x)))
(c) (2 points) d100
dt100 sin(2t−π)
Hint: What is the fourth derivative of the function?
2. (6 points) Find all points on the curve
y2+ 3x2−xy = 11
whose tangent line is horizontal.
Document Summary
Instructions: read each question carefully, and answer each question completely, show all of your work. No credit will be given for unsupported answers: write your solutions clearly and legibly. No credit will be given for illegible solutions. pts. 8 (cid:6: evaluate the following derivatives. (a) (2 points) d d(cid:18) sin((cid:18)) cos((cid:18)) tan((cid:18)) (b) (2 points) d dx sin(cos(tan(x))) (c) (2 points) d100 dt100 sin(2t (cid:0) (cid:25)) Why: at at certain time, car b is 30 miles directly east of car a and begins moving west at 90 mph. Remember to include units of measurement in your answer. (b) (3 points) at what time is the distance between the cars at a minimum: let f (x) be the following piecewise function. Explain. (c) (2 points) given your answer to (b), use the de nition of the derivative to nd f (0) or show that it doesn"t exist: let f (x) = x5 (cid:0) 4.
