First and Second Derivative Tests Flashcard

Front

The concavity of a function is described by its _______________.

Back

second derivative

Front

The slope of a function is described by its ____________.

Back

first derivative

Front

If a function's FIRST derivative is negative at a certain point, what does that tell you?

Back

The function is decreasing at that point.

Front

If f '(3) = 0 and f"(3) < 0, then which of the following must be true?

Back

There is a local max at x=3.

Front

Over what interval(s) is f(x) decreasing?

Back

(-3, 1)

Front

What does the first derivative test help determine?

Back

It helps determine local maxima and minima of a function.

Front

What does a positive second derivative indicate about a function's concavity?

Back

The function is concave up.

Front

What does a negative second derivative indicate about a function's concavity?

Back

The function is concave down.

Front

If f '(x) changes from positive to negative at x = c, what can be concluded?

Back

There is a local maximum at x = c.

Front

If f '(x) changes from negative to positive at x = c, what can be concluded?

Back

There is a local minimum at x = c.