## Review for Second part (section 007)

Note from the instructor: This review exam is not very representative of the second part of the course. It touches but a small portion of the material taught in this important part. I don’t feel this is a good study guide.

Things I miss in this exam, and will surely be part of the final: (1) Product rule. (2) Quotient rule. (3) Marginal Cost, Revenue and Profit. (4) Concavity and inflection points. (5) First and second derivative tests. (6) Interpretation of the derivative (other than slopes). (7) Optimization story problems.

1. Find the inflection points of the following functions
1. $y=2x^3-3x^2-36x+5$
2. $x^4+x^3-3x^2+2$
2. Compute the following slopes:
1. $f(x)=6x^2-4x+36$ at $(3,6)$
2. $f(x)=x^3-8x^2+2x+40$ at $(2,7)$
3. Find the intervals of increase and decrease for the following functions:
1. $f(x)=x^3-9x^2-48x+52$
2. $f(x)=x^2-11x+3$
4. Compute the derivative of the following functions
1. $6e^{5x}+e^{-x^2}$
2. $\sqrt{1-x^2}$
5. Find the absolute maximum and minimum of the function $f(x)=(x-3)(x+2)$ on the interval $[-5,2]$