Application of derivatives

Front

What does a positive second derivative indicate about a function?

Back

The function is concave up.

Front

How many extrema can a function have?

Back

A function can have multiple extrema, depending on its shape and behavior.

Front

What does a negative first derivative tell you about a function?

Back

The function is decreasing.

Front

If the velocity of an object is given as v = 2t + 3t^3, how do you find the acceleration?

Back

Take the derivative of the velocity function with respect to time.

Front

What is the instantaneous velocity of a particle at a specific time?

Back

It is the value of the first derivative of the position function at that time.

Front

What does a zero first derivative indicate about a function?

Back

The function may have a local maximum, local minimum, or a point of inflection.

Front

How do you determine concavity using the second derivative?

Back

If the second derivative is positive, the function is concave up; if negative, concave down.

Front

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

Back

If the first derivative is positive, the function is increasing; if negative, it is decreasing.

Front

How can you find the acceleration from a position function?

Back

Differentiate the position function twice with respect to time.

Front

What is the significance of critical points in a function?

Back

Critical points are where the first derivative is zero or undefined, indicating potential extrema.