🦃 5.4 First Derivative Test

• A relative maximum at x=a

• A relative minimum at x=a

• No relative extrema at x=a

• A vertical tangent line at x=a

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

• True

• False

• a relative maximum at x=a

• a relative minimum at x=a

• no relative extrema at x=a

• a vertical tangent line at x=a

• decreasing

• increasing

• concave up

• constant

Where does the function, f(x) = 2x³ - 9x² + 12x -3 have relative max/min values?

• Rel max x = -1, Rel min x = 2

• Rel min x = 1, Rel min x = 2

• Rel max x = 1, Rel min x = 2

• Rel max x = 2, Rel min x = 1

• unknown

• local maximum

• local minimum

• stationary point/platuae point

The figure shows the graph of f′, the derivative of a function f. The domain of f is the set of all real numbers x such that −3 < x < 5.

For what values of x does f have a relative maximum?

(a)  

If a function's FIRST derivative is negative at a certain point, what does that tell you?

• The function is increasing at that point
• The function is decreasing at that point
• The concavity of the function is up at that point
• The concavity of the function is down at that point