Finding X and Y Intercepts / Maximum / Minimum / Increasing / Decreasing

When the derivative of a function changes from negative to positive at x=a, this implies that a is a...

• relative minimum

• relative maximum

• point of inflection

• x-intercept

Answer explanation

When a function changes from negative to positive, there is a relative minimum. When a function changes from positive to negative, there is a relative maximum.

If f'(a) = 0 and f''(a) > 0, then x = a is a...

• relative minimum

• relative maximum

• inflection point

• x-intercept

Answer explanation

A critical point can be plugged into the second derivative to determine its concavity. If it is concave up (f''(a) is positive), the critical point is a minimum. If it is concave down (f''(a) is negative), the critical point is a maximum.

In optimization problems, you are really finding...

• x-intercepts

• extrema

• points of inflection

• volume formulas

When a function is increasing, the derivative is...

• increasing

• positive

• concave up

• constant

Answer explanation

When a function is increasing the derivative is positive. This means that for the x-values that the graph is increasing, the graph of the derivative will be above the x-axis. The inverse is true for decreasing areas of a function.

Tags

CCSS.HSF.IF.B.4

Only type one number.

Mathematical Equivalence

ON

Tags

CCSS.HSF-IF.C.7A

A graph of a quadratic function is shown. What is/are the x-intercept(s) of the function?

Tags

CCSS.HSF-IF.C.7A

A graph of a quadratic function is shown. What is the y-intercept of the function?

Tags

CCSS.HSF-IF.C.7A

What are the x- intercepts?

• x= 0 and x= -4

• x= 0 and x= 4

• y= 0

• x= 2

Tags

CCSS.HSF-IF.C.7A

What are the x-intercepts (solutions)?

• (-2,0) and (2,0)

• (0,-4)

• (-2,-4) and (2,-4)

Tags

CCSS.HSF-IF.C.7A

A graph of a quadratic function is shown. What is the vertex of the function?