derivatives

1. Find the derivatives of each of the following functions:

1. $y = 3x + 5$
2. $y = -5x - 12$
3. $y = 3x^2 + 5 $
4. $y = -4x^2 + 5x - 7$
5. $y = 6x^5 + 5x^4 - 8x^3 + 7x^2 - 8x + 5$

2. Suppose your profit when you sell 1000 units is \$5000, and that the derivative of ...

1. For the equation $y = x^2 + 3 $ :

1. Find the average slope between $x = 2 $ and $ x = 4$
2. Find the average slope between $x = -4 $ and $ x = -2$
3. Find the average slope between $x = -2 $ and $ x = 2$
4. Determine what value of x will give a slope of zero.

Solution:

1. $\frac ...

intro to calculus

Linear inequalities

1. Rearrange the following to determine allowed values for y:
   1. $$ 2y + 3 < 10 $$
   2. $$ -3y -5 > 6 $$
2. Rearrange to find allowed values for y in terms of x:
   1. $$ 2y + 3x < 10 $$
   2. $$ -3y - 5x + 7 > 2 $$
3. Sketch graphs of the two inequalities given in #2, and shade in the region of the plane ...

Matrix inverses and linear inequalities