(2. Use the graph of y=f(x) in Figure 1 to answer each of the following parts.
Figure 1: Problem 2
(a) Estimate the value(s) of x such that f'(x)=0.
(b) Estimate the value(s) of x such that f''(x)=0.
(c) Sketch the graph of f'(x).
(d) Sketch the graph of f''(x).
The average weight, W, in pounds, of an adult is a function, W=f(c), of the average Calories per day, c, consumed.
(a) Interpret the statement f(1800)=155.
(b) Interpret the statement f'(2000)=0.
(c) What are the units of f'(c)?
If it is known that f(3)=6 and f'(3)=5:
(a) Estimate f(4).
(b) Estimate f(0).
(c) Give an equation for the line tangent to the line at x=3.
Determine if each of the following statements are true or false.
(a) If f is negative on an interval, then the derivative of f is decreasing on that interval.
(b) If f is always increasing, then f'(x) is always increasing.
(c) If y=f(x), then f'(x) and (dy)/(dx) mean the same thing.
(d) A function can have more than one point where its derivative is equal to 0.