What does taking the derivative of a function tell you about the
function? Is a derivative a local property in the sense that you
can define the derivative of a function f(x) at x?
What does integrating a function tell you? Is an integral a
local property in the sense that you can define the integral of a
function f(x) at x?
If you first differentiate a function and then integrate it, are
you going to get the same function...
Consider functions f : {1,2,3,4}→{1,2,3,4,5,6}.
a) Give an example of one such function (use 2-line notation).
Then say how many such functions there are and why your answer
makes sense.(25 points)
(b)Give one example of such a function that is injective and one
that is not. Then say how many injective functions there are and
why your answer makes sense.(50 points)
(c) Explain why there are no surjective functions with this
domain and codomain. (25 points)
The notation used in the above problem is called symbolic
notation. Alternatively, we can use the 4-digit octal notation to
specify, which is defined as follows: • Digits from left (most
significant) to right (least significant): [special bits][owner
bits][group bits][world bits] • Special bit digit = (4 if setuid) +
(2 if setgid) + (1 if sticky), 0 for none of them • All other
digits = (4 if readable) + (2 if writable) + (1 if executable), 0
for...
A. Use the Product Rule or the Quotient Rule to find the
derivative of the function.
g(x) = x3 cot(x) + 6x cos(x)
B. Use the Product Rule or the Quotient Rule to find the
derivative of the function.
f(x) =
x2 + x − 7
x2 − 7
C. Use the Product Rule or the Quotient Rule to find the
derivative of the function.
f(x) = (8x2 + 4)(x2 − 6x − 9)
Use the given function, its first derivative, and its second
derivative to answer the following:
f(x)=(1/3)x^3 - (1/2)x^2 - 6x + 5
f'(x)= x^2 - x - 6 = (x+2)(x-3)
f''(x)= 2x - 1
a) What are the intervals of increase and the intervals of
decrease
b) Identify local min and max points
c) What are the intervals where the function is concave up,
concave down and identify the inflection points