Using the First Derivative Test in Calculus

Front

The slope of a function is described by its ____________.

Back

first derivative

Front

Use the sign chart for f'(x). There is(are) ...

Back

a local maximum at x = -2 and a local minimum at x = 4.

Front

If the first derivative of a function changes from positive to negative at a certain point, then that point is known as a ____________.

Back

relative maximum.

Front

If the 1st derivative is positive on a certain interval, then that interval is ____________.

Back

increasing.

Front

Using the FIRST DERIVATIVE TEST, algebraically determine the intervals: What is the result?

Back

local maximum at x = -4 (no local minimum).

Front

What does the First Derivative Test help determine?

Back

It helps identify local maxima and minima of a function.

Front

If f'(x) > 0, what can be said about the function f(x)?

Back

The function f(x) is increasing.

Front

If f'(x) < 0, what can be said about the function f(x)?

Back

The function f(x) is decreasing.

Front

What is the significance of critical points in relation to the first derivative?

Back

Critical points occur where f'(x) = 0 or f'(x) is undefined, indicating potential local extrema.

Front

What does a sign change from negative to positive in f'(x) indicate?

Back

It indicates a local minimum at that point.