Unit 6- Week 3- First Derivative Test

Refer to the graph and the information below.

The function f is defined on the closed interval [0,8]. The graph of its derivative f' is shown above.

At what value of x does the absolute minimum of f occur?

• 0

• 2

• 4

• 6

• 8

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)  

Over what interval(s) is f(x) increasing?

• (-∞, -3) ∪ (1, ∞)
• (-3, 1)
• (-5, 0) ∪ (2, ∞)
• (-5, ∞)

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

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

Tags

CCSS.8.EE.B.5

Use the sign chart for f'(x).  There is(are) ...

• a local maximum at x = -2.
• a local minimum at
  x = -2 and a local maximum at x = 4.
• a local maximum at
  x = -2 and a local minimum at x = 4.
• no extrema.

Over what intervals is f(x) decreasing?

• (-∞, -1) ∪ (1, ∞)

• (-∞, -√3) ∪ (0, √3)

• (-1, 1)

• (-√3, 0) ∪ (√3, ∞)

• -1 , 0 , -1.5
• -1 , 0
• -1 , 2/3
• -1 , 0 , 1.5

Find the second derivative of the function:
f (x) =  2x - 5x⁶

• f ''(x)= 2 - 30x
• f ''(x) =  2-30x⁵
• f ''(x) = -30x⁵
• f ''(x) = -150x⁴

Find the derivative of y = 2x² (3x - 4)

• 6x³ - 8x²
• 18x² - 16x
• 15x² - 6x
• 6x - 4