Unit 5 Review

Front

What is a point of inflection?

Back

A point of inflection is where a function changes from concave up to concave down or vice versa.

Front

If a function has a second derivative that is negative, what does that tell you?

Back

If a function has a second derivative that is negative, it indicates that the function is concave down.

Front

Where does the function, f(x) = 2x^3 - 9x^2 + 12x - 3 have relative max/min values?

Back

Relative max at x = 1, Relative min at x = 2.

Front

What is the maximum value of f(x) = x^3 - 3x^2 - 1 on the interval [-3, 2]?

Back

The maximum value is -1.

Front

Given a function, f(x), if f'(x) > 0 over a certain interval, then f(x) is __________ over that interval.

Back

increasing.

Front

What does it mean if a function is concave up?

Back

A function is concave up if its second derivative is positive, indicating that the slope of the function is increasing.

Front

What is the first derivative test used for?

Back

The first derivative test is used to determine the local maxima and minima of a function.

Front

How do you find the critical points of a function?

Back

Critical points are found by setting the first derivative of the function equal to zero and solving for x.

Front

What is the significance of a local maximum?

Back

A local maximum is a point where the function value is higher than all nearby points.

Front

What is the significance of a local minimum?

Back

A local minimum is a point where the function value is lower than all nearby points.