Podcast
Questions and Answers
If a function is concave up on an interval, what kind of point can it have in that interval?
If a function is concave up on an interval, what kind of point can it have in that interval?
Local minimum
What is the significance of a critical number of a function?
What is the significance of a critical number of a function?
It could be a possible location for a local maximum, local minimum, or an inflection point.
How does changing the domain of a function affect its function values?
How does changing the domain of a function affect its function values?
It can change the range of the function but may not affect the function's critical points.
What can be said about the absolute maximum and minimum values of a function on a closed interval?
What can be said about the absolute maximum and minimum values of a function on a closed interval?
How can inflection points be identified on a graph?
How can inflection points be identified on a graph?
What is the purpose of finding critical numbers of a function?
What is the purpose of finding critical numbers of a function?
Provide an example of a function f where at least one of the hypotheses of Rolle's theorem is not satisfied on the interval [a, b], but f has a horizontal tangent at x = c where c is in (a, b).
Provide an example of a function f where at least one of the hypotheses of Rolle's theorem is not satisfied on the interval [a, b], but f has a horizontal tangent at x = c where c is in (a, b).
Give an example of a function g defined on [-4, 4] that meets the following criteria: no absolute maximum, exactly one local maximum, an absolute minimum, no local minimum, and exactly 2 critical values.
Give an example of a function g defined on [-4, 4] that meets the following criteria: no absolute maximum, exactly one local maximum, an absolute minimum, no local minimum, and exactly 2 critical values.
Explain how changing the domain of a function can affect the function's values.
Explain how changing the domain of a function can affect the function's values.
What is an inflection point on a graph? Provide a brief explanation.
What is an inflection point on a graph? Provide a brief explanation.
Define what an absolute maximum and an absolute minimum are for a function.
Define what an absolute maximum and an absolute minimum are for a function.
What are critical numbers of a function? Provide a simple explanation.
What are critical numbers of a function? Provide a simple explanation.
State one method to find the temperature at which the engine is heating up the fastest.
State one method to find the temperature at which the engine is heating up the fastest.
If f has only a local minimum at x=1, what type of extrema does g(x) have on [1,5]?
If f has only a local minimum at x=1, what type of extrema does g(x) have on [1,5]?
Which statement among the given choices must be false?
Which statement among the given choices must be false?
