Applications of Derivatives Review

Front

What occurs when a function switches from increasing to decreasing?

Back

Relative maximum

Front

What does a positive second derivative indicate about a function?

Back

The function is concave up

Front

Find the x-coordinate of the inflection point of the function f(x)=6x^2-x^3.

Back

2

Front

What is the value of f'(1) for the function f(x)=\sqrt{1-x^2}?

Back

DNE (Does Not Exist)

Front

What is true at an inflection point?

Back

f''(x)=0

Front

What is the definition of a relative maximum?

Back

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

Front

What does the first derivative test help determine?

Back

Whether a function is increasing or decreasing at a given point.

Front

What is the significance of a critical point?

Back

It is where the first derivative is zero or undefined.

Front

What does a negative second derivative indicate about a function?

Back

The function is concave down.

Front

How do you find the inflection points of a function?

Back

Set the second derivative equal to zero and solve for x.