104/184 Quiz #4
November 20
Grade:
First Name:
Last Name:
Student-No:
Section:
Very short answer questions
1. 2 marks Each part is worth 1 mark. Below is a graph of f 0 (x), the derivative of f (x).
(a) When is f (x) increasing?
Answer:
(b) When does f (x) have an inflection point?
Answer:
Short answer questions — you must show your work
2. 4 marks Each part is worth 2 marks.
(a) When is the function g(x) = 3x4 + 4x3 concave up?
Answer:
x2 − 9
(b) Suppose that f (x) is a function with derivative f (x) =
. Determine whether
(2x − 7)
there is a local maximum or minimum value (or neither) at x = 3.
0
Answer:
Long answer question — you must show your work
3. 4 marks Consider the function
which has derivatives
f 0 (x) =
√
f (x) = (x − 3) x,
3 x+1
3 x−1
· √ and f 00 (x) = · 3/2 .
2
4 x
x
(a) When is f(x) increasing and decreasing?
(b) When is f(x) concave up or concave down?
(c) Sketch the graph of f (x). Clearly label any extreme values and inflection points (if any).
104/184 Quiz #4
November 20
First Name:
Last Name:
Student-No:
Section:
Grade:
Very short answer questions
1. 2 marks Each part is worth 1 mark. Below is a graph of f 0 (x), the derivative of f (x).
(a) Where is f (x) decreasing?
Answer:
(b) Where does f (x) have an inflection point?
Answer:
Short answer questions — you must show your work
2. 4 marks Each part is worth 2 marks.
(a) When is the function g(x) = 3x4 + 4x3 concave down?
Answer:
x2 − 9
. Determine whether
(2x − 7)
there is a local maximum or minimum value (or neither) at x = −3.
(b) Suppose that f (x) is a function with derivative f 0 (x) =
Answer:
Long answer question — you must show your work
3. 4 marks Consider the function
which has derivatives
f 0 (x) =
√
f (x) = (x − 6) x,
3 x+2
3 x−2
· √ and f 00 (x) = · 3/2 .
2
4 x
x
(a) When is f(x) increasing and decreasing?
(b) When is f(x) concave up or concave down?
(c) Sketch the graph of f (x). Clearly label any extreme values and inflection points.
104/184 Quiz #4
November 20
First Name:
Last Name:
Student-No:
Section:
Grade:
Very short answer questions
1. 2 marks Each part is worth 1 mark. Below is a graph of f 0 (x), the derivative of f (x).
(a) When is f (x) increasing?
Answer:
(b) When does f (x) have an inflection point?
Answer:
Short answer questions — you must show your work
2. 4 marks Each part is worth 2 marks.
(a) When is the function g(x) = 3x4 − 4x3 concave up?
Answer:
9 − x2
. Determine whether
(2x − 7)
there is a local maximum or minimum value (or neither) at x = 3.
(b) Suppose that f (x) is a function with derivative f 0 (x) =
Answer:
Long answer question — you must show your work
3. 4 marks Consider the function
√
f (x) = (x) x + 3,
which has derivatives
f 0 (x) =
3
x+4
3 x+2
and f 00 (x) = ·
·√
.
2
4 (x + 3)3/2
x+3
(a) When is f(x) increasing and decreasing?
(b) When is f(x) concave up or concave down?
(c) Sketch the graph of f (x). Clearly label any extreme values and inflection points.
104/184 Quiz #4
November 20
First Name:
Last Name:
Student-No:
Section:
Grade:
Very short answer questions
1. 2 marks Each part is worth 1 mark. Below is a graph of f 0 (x), the derivative of f (x).
(a) When is f (x) decreasing?
Answer:
(b) When does f (x) have an inflection point?
Answer:
Short answer questions — you must show your work
2. 4 marks Each part is worth 2 marks.
(a) When is the function g(x) = 3x4 − 4x3 concave down?
Answer:
9 − x2
. Determine whether
(2x − 7)
there is a local maximum or minimum value (or neither) at x = −3.
(b) Suppose that f (x) is a function with derivative f 0 (x) =
Answer:
Long answer question — you must show your work
3. 4 marks Consider the function
√
f (x) = (x) x + 6,
which has derivatives
f 0 (x) =
3
x+8
3 x+4
and f 00 (x) = ·
·√
.
2
4 (x + 6)3/2
x+6
(a) When is f(x) increasing and decreasing?
(b) When is f(x) concave up or concave down?
(c) Sketch the graph of f (x). Clearly label any extreme values and inflection points.