(a) How do you find the second derivative of a function?
(b) If both are positive numbers, what does that tell you about the function itself?
(c) If we know that a function is increasing, but at a decreasing rate, what does that say about the first and second derivatives?
(d) Come up with a function where the first and second derivatives are non-zero but the third derivative is zero.
Find the local maximum and minimum values of the function.
Tell the intervals where the graph of the function is increasing
and decreasing
f(x)= 2x^3 +3x^2 - 12x
1) The graph of the derivative f ' of a continuous function f is
shown. (Assume the function f is defined only for 0 < x <
∞.)
(a) On what interval(s) is f increasing? (2a) On what
interval(s) is f decreasing?
(b) At what value(s) of x does f have a local
maximum? (2b) At what value(s) of x does f have a
local minimum? x=?
(c) On what interval(s) is f concave upward? (2c) On
what interval(s) is...
Describe how you could use a turbidity measurement to tell how
many colonies you would expect from plating a culture of a given
OD.
Escherichia coli can grow at a higher temperature in a
complex medium than in a defined medium. Why?
What is Taq polymerase and why is important?
If given the spectra for 2-Heptanone and Heptanal, how could you
tell which is which?
If given the spectra for 2-Heptanone and Heptanoic Acid, how
could you tell which is which?
If given the spectra for Tetrahydrofuran and 2-heptanol, how
could you tell which is which?
If given the spectra for tetrahydrofuran and ethyl pentanoate,
how couldm you tell which is which?
1. Explain how the first derivative test of a function determines where the function is increasing and decreasing.2. Explain how to apply the second derivative test.3. What is an inflection point?4. Why are special methods such as L'Hopital's Rules, needed to evaluate indeterminate forms?
How can you tell what kind of market structure something is by
only looking at a graph that shows demand, marginal revenue (in the
short and logn run) and marginal cost and average cost? What do you
look for to determine the type of market structure that it is?