Chapter 9.2, Problem 56E

What is the purpose of the Intermediate Value Theorem?

Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.

false: If f(x) is differentiable in its domain then True or f must be continuous in its domain?

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Suppose f is a continuous function on [a,b] and suppose that f(a) < 0 and f(b) > 0 What can you say about the number of times that the graph of f crosses the x-axis? What about the number of times the graph of f touches the x-axis? Explain your reasoning.