5-3 & 5-4 The First Derivative Test

5-3 & 5-4 The First Derivative Test

Guided Notes

Multiple Choice

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

Multiple Choice

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

Multiple Choice

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

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

Multiple Choice

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

• (-∞, -3) ∪ (1, ∞)

• (-3, 1)

• (-5, 0) ∪ (2, ∞)

• (-5, ∞)

Multiple Choice

Over what intervals is f(x) decreasing?

• (-∞, -1) ∪ (1, ∞)

• (-∞, -√3) ∪ (0, √3)

• (-1, 1)

• (-√3, 0) ∪ (√3, ∞)

Multiple Choice

If  $$f'\left(x\right)=0$$  and  $$f'\left(a\right)=0$$  changes from negative to positive at $$f'\left(x\right)$$  , then  $$x=a$$  has

• 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

Multiple Choice

If  $$f'\left(x\right)$$  and  $$f'\left(x\right)$$  changes from positive to negative at  $$x=a$$  , then  $$f\left(x\right)$$  has 

• 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

Multiple Choice

The function  $$f\left(x\right)=-x^3+3x^2-5$$  has a relative maximum value of _____________ at x=_____________.

• 0; -5

• -5; 0

• 2; -1

• -1; 2

Multiple Choice

If  $$\ f'\left(a\right)=0$$  , then you are guaranteed a relative extreme value at x=a. 

• True

• False

Multiple Choice

Which of the following could be the graph of f ' , the derivative of f ?