Exam Logistics
What section number are we?
049
List all cases where a function is not differentiable.
A corner or a cusp, vertical tangent line, or not continuous at the point.
The tangent line approximation is a overestimate when f(x) is _____.
concave down
f'(x) = 0 or f'(x) DNE
How does the constraint function help us in optimization problems?
Allows us to write the optimization function (or function we are finding the min/max of) in terms of one variable.
What time does the exam begin?
8:15 p.m.
What are two things we need to check for differentiability of function?
(1) continuity (set the functions equal)
(2) derivative exists (set the derivatives equal)
(especially at points were the piecewise function changes from one function to another)
What is the hypothesis of the Mean Value Theorem?
f(x) is continuous on [a, b], and f(x) is differentiable on (a, b).
How do we determine if a candidate inflection point is an actual inflection point?
In related rates problem, once we take the derivative of the relevant equation what should we do?
Identify known rates and variables, plug them in to solve for the unknown related rate.
What building and room is our section in?
CHEM 1800
(unless you have an SSD accommodation)
Give the correct formula for d/dx (f^-1(x)), or the derivative of the inverse function.
1/f'(f^-1(x))
What is the hypothesis of the Extreme Value Theorem?
f is continuous on a closed interval [a, b]
Find all critical points of q(x) if q'(x) = x^(2/3)*(x-3)^(5/3)(x+5). Determine the local maxes and mins.
x = 0, 3, -5
Local Max: at x = -5
Local Min: at x = 3
The hour and minute hands of a clock move continuously in the clockwise direction, with the minute hand making one complete revolution every hour and the hour hand making one complete revolution every 12 hours.If theta is the radian measure of the angle between the two hands, what is d(theta)/dt at 3 pm in radians per hour?
-11*pi/6
What are three things you should bring to the exam?
Pencils, MCard, and 3'' x 5'' notecard, mask (optional)
Consider the family of ellipses C defined implicitly by the equation k^-4*x^2 + e^2k*y^2 = 1 where k>0, find the unique value of k such that the point (0, 1/2) lies on the ellipse C.
ln(2)
What is the conclusion of the Extreme Value Theorem?
f has a global maximum and a global minimum on the interval.
Let f(x) = -2e^(2x-2) for x <= 1 and x^3 - 3x^2 for x > 1.
Find the x-coordinate of all global maxima and minima of f(x) on the interval (-infinity, 4].
Global Maxes: x = 4
Global Mins: x = 2
Suppose a spherical snowball is melting so that its surface area decreases at the constant rate of 20 cm^2 per minute. How fast is the radius of the snowball changing when the radius is 5 cm?
Surface Area S of a sphere: 4 * pi * r^2
What percentage of your grade is Exam 2 worth?
20%
What is the conclusion of the Mean Value Theorem?
There exists a c in [a, b], such that f'(c) = (f(b) - f(a))/(b-a)