104/184 Quiz #4
November 19
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) concave up?
Answer:
(b) Where does f (x) have a local maximum?
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) = xe3x increasing?
Answer:
(b) Suppose that f (x) is a function with f 0 (π) = 0 and f 00 (x) =
x2 − 9
. Determine
2x · (2x − 3)
whether there is a local maximum or minimum value at x = π.
Answer:
Long answer question — you must show your work
3. 4 marks Consider the function
f (x) = (x + 1)(x − 2)2 ,
which has derivatives
f 0 (x) = 3x(x − 2) and f 00 (x) = 6(x − 1).
(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 19
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) concave down?
Answer:
(b) Where does f (x) have a local minimum?
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) = xe4x increasing?
Answer:
(b) Suppose that f (x) is a function with f 0 (π) = 0 and f 00 (x) =
9 − x2
. Determine
2x · (2x − 3)
whether there is a local maximum or minimum value at x = π.
Answer:
Long answer question — you must show your work
3. 4 marks Consider the function
f (x) = (x − 1)(x + 2)2 ,
which has derivatives
f 0 (x) = 3x(x + 2) and f 00 (x) = 6(x + 1).
(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 19
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) concave up?
Answer:
(b) Where does f (x) have a local maximum?
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) = xe5x increasing?
Answer:
(b) Suppose that f (x) is a function with f 0 (π) = 0 and f 00 (x) =
x2 + 9
. Determine
2x · (2x − 6)
whether there is a local maximum or minimum value at x = π.
Answer:
Long answer question — you must show your work
3. 4 marks Consider the function
f (x) = (x + 1)2 (x − 2),
which has derivatives
f 0 (x) = 3(x2 − 1) and f 00 (x) = 6x.
(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 19
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) concave down?
Answer:
(b) Where does f (x) have a local minimum?
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) = xe6x increasing?
Answer:
(b) Suppose that f (x) is a function with f 0 (π) = 0 and f 00 (x) =
x2 + 9
. Determine
2x · (6 − 2x)
whether there is a local maximum or minimum value at x = π.
Answer:
Long answer question — you must show your work
3. 4 marks Consider the function
f (x) = (x + 2)(x − 1)2 ,
which has derivatives
f 0 (x) = 3(x2 − 1) and f 00 (x) = 6x.
(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.