Unit 5 Test Review AB

Front

What indicates a relative minimum for a function y?

Back

y' changes from - to +.

Front

What indicates a relative maximum for a function y?

Back

y' changes from + to -.

Front

Does the Mean Value Theorem apply to a function f on a closed interval [a, b]?

Back

No, it does not apply if the function is not continuous or differentiable on that interval.

Front

What are the local extrema for the function f(x) = x^3 + 3x^2 - 24x?

Back

Minimum point: (2, -28) and maximum point: (-4, 80).

Front

What is the purpose of the second derivative test in calculus optimization?

Back

It is used to determine whether a critical point is a maximum, minimum, or saddle point.

Front

What does it mean when y' = 0 at a point?

Back

It indicates a potential critical point where the function may have a local maximum, minimum, or saddle point.

Front

What is the definition of a critical point in calculus?

Back

A critical point is where the derivative is zero or undefined.

Front

How do you determine the concavity of a function?

Back

By using the second derivative; if f''(x) > 0, the function is concave up; if f''(x) < 0, it is concave down.

Front

What is the relationship between the first derivative and increasing/decreasing functions?

Back

If y' > 0, the function is increasing; if y' < 0, the function is decreasing.

Front

What is the significance of the first derivative test?

Back

It helps to determine the local extrema of a function by analyzing the sign changes of the first derivative.