Determine whether each statement is true or false, and explain why. The derivative in regions separated by critical numbers must alternate between positive and negative. A relative maximum is the greatest possible value of a function. A function has relative extrema at all critical numbers of the function. If a function is concave upward on an interval, it must be increasing on that interval. Acceleration is the instantaneous rate of change of velocity. If a function has an inflection point at x = c, then f"(c) = 0.

How are the absolute maximum and minimum similar to and different from the local extrema?

Use the table of values you made in part 4 of the example to find the limiting value of the average rate of change in velocity.

If xis large, which function grows faster, f(x)=2x or g(x)=x2?

Are one-to-one functions either always increasing or always decreasing? Why or why not?

The half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14 remaining as a function of time, measured in years.

When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal compression from a vertical compression?

Water temperature in a river is being modeled as a function of air temperature. If the degrees of freedom for error is 9, R2 = 0.4, and SSE = 200, if the estimated coefficient of air temperature is 0.8, what is the standard error for the coefficient of air temperature? Please report your answer in 3 decimal places.