Calculus Answers

If zxy=−5x, what can you say about each of the following?

(a) zyx =

(b) zxyx =

(c) zxyy =

A price p (in dollars) and demand x for a product are related by
2x^2−3xp+50p^2=23600.

If the price is increasing at a rate of 2 dollars per month when the price is 20 dollars, find the rate of change of the demand

Suppose that for a company manufacturing calculators, the cost, and revenue equations are given by
C=70000+40x,R=400−x^2/20,
where the production output in one week is x calculators. If the production rate is increasing at a rate of 500 calculators when the production output is 6000 calculators, find each of the following:

Rate of change in cost =

Rate of change in revenue =

Rate of change in profit =

Sketch one graph of a function g that has no absolute maximum, no absolute minimum, and one local maximum

For the graph of y = bx, the domain is?

What is the y-intercept for the exponential function y = bx ?

Find one set of values of the numbers a and b, such that the function y = e^(ax) + bln(x) is a solution of the differential equations given below.

a. y^n - ay' = 0

b. y' + y - (b/x) = 0

Find the absolute max and min of the function f(x) = (x)/(x^(2) + 4) on the interval [0,4].

Sketch one graph of a single function f that satisfies all of the conditions below

a. domain (0, infinity)
b. limit as x -> 0+ f(x) = infinity
c. limit as x-> infinity f(x) = 2
d. f'(x) < 0 on the interval (0,3)
e. f'(x) > 0 on the interval (3, infinity)
f. f'(3) = 0
g. f''(x) > 0 on the interval (0,6)
h. f''(x) < 0 on the interval (6, infinity)

The polynomial f(x)=2x^3+5x^2+3 is given. Find f(1.5), f'(1.5), f''(1.5), f'''(1.5) using synthetic division.