Math Answers

The derivative of a differentiable function ff(xx) is given as

ff′

(xx) = xx + 3

(xx − 2)2 .

a. Find intervals of increase and decrease for ff(xx).

b. Determine values of xx for which relative maxima and minima occurs on the graph of

ff(xx).

c. Find ff′′(xx) and determine intervals of concavity for the graph of ff(xx).

d. For what values of xx do inflection points occur on the graph of ff(xx).

Suppose that a population yy grows according to the logistic model given by formula:

yy = LL

1 + AAee−kkkk .

a. At what rate is yy increasing at time tt = 0 ?

b. In words, describe how the rate of growth of yy varies with time.

c. At what time is the population growing most rapidly?

How to calculate cos x from its nth term in Maclaurin series??

1.Convert the polar coordinates (-8, ) into rectangular coordinates.

2.Convert the rectangular coordinates (3, -3) into polar coordinates with r > 0 and 0 ≤ θ < 2π.

3.Convert the rectangular equation x2 + y2 = 100 into a polar equation that expresses r in terms of θ.

4.Convert the polar equation 4r cos θ + r sin θ = 8 into a rectangular equation that expresses y in terms of x.

Plot the following points:

P1 (-3, 135°)

P2 (2, )

P3 (4, 405°)

Graph

Sketch the graph of r = 3 − 2cosθ.

Find the equations of the tangents and normal to the following curves:

1. y2 + 8x = 0, parallel to x + y + 4 = 0.

2. x2 = 3y, perpendicular to x – 2y + 7 = 0.

3. x2 + 9y2 = 25, parallel to 4x + 9y + 30 = 0.

4. 25x2 + 4y2 = 100, perpendicular to 8x – 15y + 4 = 0.

5. x2 – y2 = 15, parallel to 4x – y + 20 = 0.

Financial goals should be one of your top priority when you graduate from senior highschool. How would the concept of simple and compound interest work on your favor to make sound decisions to achieve financial goals?

A certain area of the eastern United States is, on average, hit by 6 hurricanes a year. Find the probability that in a given year that area will be hit by

(a) fewer than 4 hurricanes;

(b) anywhere from 6 to 8 hurricanes.

the burr distribution has a probability function for a continuous random variable x given by f(x)={(ckx^c-1)/(1+x^c)^k+1 x>o 0 otherwise} show that the E(x) = kB(k+1/c,1/c+1)

A probability density function of a discrete random variable x is given by

f(x)={(1/2)^x x=1,2,3,... 0 elsewhere}

use pgf to find a)E(x) b)V(x)