Practice with the First Derivative Test

Front

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

Back

False (Not Facts). If the first derivative is positive, the function is increasing on that interval.

Front

On what interval(s) is f increasing if f'(x) is positive?

Back

f is increasing on the interval [-1,2].

Front

For a function f(x), if f'(-3) = 5, what does this indicate about f(x) at x=-3?

Back

f(x) is increasing at x=-3.

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Back

Front

Back

Front

What is the First Derivative Test?

Back

A method to determine local maxima and minima by analyzing the sign of the first derivative before and after critical points.

Front

Define a critical point in the context of calculus.

Back

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

Front

What does it mean if the first derivative changes from positive to negative at a critical point?

Back

It indicates a local maximum at that critical point.

Front

What does it mean if the first derivative changes from negative to positive at a critical point?

Back

It indicates a local minimum at that critical point.

Front

What is Rolle's Theorem?

Back

If a function is continuous on a closed interval and differentiable on the open interval, then there exists at least one point c in the interval where the derivative is zero.