Question 1

Draw a graph of the following linear equation, \(R=4-\frac{1}{2}W\). Plot \(W\) on the vertical axis and \(R\) on the horizontal axis.

Question 2

Draw a continuous function which begins at the origin, increases at a decreasing rate, reaches an inflection point, and then increases at an increasing rate. Show where each part of the function is concave or convex.

Question 3

Solve the system of equations for \(x\) and \(y\):

\[\begin{align*} 2x+y&=20\\ 4x-3y&=10\\ \end{align*}\]

Question 4

Simplify the following equation:

\[Z=\frac{0.5X^{-0.5} Y^{0.5}}{0.5X^{0.5}Y^{-0.5}}\]

Question 5

For the function \(f(x) = 3x^2+2x-7\):

1. Take the derivative of \(f(x)\), i.e. \(f'(x)\).
2. In English, describe what the derivative of \(f(x)\) means.
3. Evaluate \(f'(4)\). In English, describe what this means.

Question 6

Find the maximum value of the function:

\[f(x)=-2x^2+16x\]

Question 7

Explain what a tangency on a curve means. What is true about the tangent line?

Question 8

On a scale of 1 (worst) to 10 (best), rate your algebra skills (i.e. solving equations, graphing lines, working with fractions, etc.).

Question 9

Have you had any experience with calculus?

Question 10

On a scale of 1 (least) to 10 (most), how anxious are you about this class? Feel free to elaborate any specific anxieties – it will make it more likely that I can specifically address them!