Calc - Given following characteristics of a function graph, answer the following questions

Question

I haven't taken Calc in a decade and this is for an accounting degree, I think I have the right answers through looking in my old book and for online help, but want to double check

• The function has 3 critical points
• When x=30, the first derivative is negative
• When x=20, the first derivative is zero
• When x=50, the first derivative is zero and the second derivative is positive
• When x=80, the first derivative is zero

Answer the following questions

1. T or F When x=40, the first derivative is positive
2. T or F When x=20 the second derivative is positive
3. T or F When x=12 the first derivative is positive
4. T or F The basic shape of this curve is more like an M than a W
5. T or F For any value of x between 50 and 80, the first derivative will always be negative

I think the answers are F, F, T, T, F.

1. False due to decreasing towards x=50 which is a minimum due to second derivative being positive

2. False due to being a critical point

3. True due to increasing towards x=20, which then decreases until x=50

4. True my graph looks like an M

5. False due to increasing from x=50 which is our minimum towards x=80 which is our 3rd critical point.

Here is the graph I sketched

Thanks