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First and Second Derivative Test

Authored by Jasmine Maneates

Mathematics

11th Grade - University

CCSS covered

Used 230+ times

First and Second Derivative Test
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12 questions

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1.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Media Image

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

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

2.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Media Image

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

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

Tags

CCSS.HSA.REI.D.10

3.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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

Tags

CCSS.HSF.IF.B.4

4.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The slope of a function is described by its ____________.

first derivative
second derivative
third derivative
expression

Tags

CCSS.HSS.ID.C.7

5.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

when you check for sign changes at the critical points of a function, you are using the

IVT

MVT

1st Derivative Test

2nd Derivative Test

6.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Media Image

Over what intervals is f(x) decreasing?

(-∞, -1) ∪ (1, ∞)
(-∞, -√3) ∪ (0, √3)
(-1, 1)
(-√3, 0) ∪ (√3, ∞)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

7.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

If (a,b) is a local maximum, then what will be true about f''(a)?

It's positive
It's negative
It's zero
Cannot be determined

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