Imagine you are sketching a curve. You find the first derivative of your function; you find where it is positive, negative, and zero; and you make a "skeleton" sketching showing areas of increase and decrease. Since this is only the first step in your sketch, you aren't particularly careful about anything other than the sign of the first derivative (positive, negative, or zero). For each skeleton below, you will select the most fitting derivative. Each skeleton below matches a function f(x) whose derivative has the form where: • a is 1 or -1, ⚫n is 1 or 2, and • m is 1 or 2. f'(x) = a(x + 1)” (x − 1)m -1 N This skeleton corresponds to a function f(x), whose derivative is ƒ'(x) = a(x + 1)”(x − 1)™, with a = 1 v, n = 2, and m = 2 v -1 This skeleton corresponds to a function f(x), whose derivative is f'(x) = a(x + 1)" (x − 1)™, with a = -1, n = 2 ✓ and m 1 Consider the following graph of a derivative f': (a) At what x-values do the points of inflection of f occur? x = (2,5) (Click on the graph to enlarge it) (Enter your answer as a value, or a comma-separated list of values, or NONE.) (b) On which interval(s) is f concave down? f is concave down for x in (-1,1) (Enter your answer using help (intervals).)
Imagine you are sketching a curve. You find the first derivative of your function; you find where it is positive, negative, and zero; and you make a "skeleton" sketching showing areas of increase and decrease. Since this is only the first step in your sketch, you aren't particularly careful about anything other than the sign of the first derivative (positive, negative, or zero). For each skeleton below, you will select the most fitting derivative. Each skeleton below matches a function f(x) whose derivative has the form where: • a is 1 or -1, ⚫n is 1 or 2, and • m is 1 or 2. f'(x) = a(x + 1)” (x − 1)m -1 N This skeleton corresponds to a function f(x), whose derivative is ƒ'(x) = a(x + 1)”(x − 1)™, with a = 1 v, n = 2, and m = 2 v -1 This skeleton corresponds to a function f(x), whose derivative is f'(x) = a(x + 1)" (x − 1)™, with a = -1, n = 2 ✓ and m 1 Consider the following graph of a derivative f': (a) At what x-values do the points of inflection of f occur? x = (2,5) (Click on the graph to enlarge it) (Enter your answer as a value, or a comma-separated list of values, or NONE.) (b) On which interval(s) is f concave down? f is concave down for x in (-1,1) (Enter your answer using help (intervals).)
Chapter2: Functions And Their Graphs
Section2.4: A Library Of Parent Functions
Problem 47E: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate...
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Transcribed Image Text:Imagine you are sketching a curve. You find the first derivative of your function; you find where it is positive, negative, and zero; and you make a "skeleton" sketching showing areas of increase and decrease. Since this is only the
first step in your sketch, you aren't particularly careful about anything other than the sign of the first derivative (positive, negative, or zero).
For each skeleton below, you will select the most fitting derivative. Each skeleton below matches a function f(x) whose derivative has the form
where:
• a is 1 or -1,
⚫n is 1 or 2, and
• m is 1 or 2.
f'(x) = a(x
+ 1)” (x − 1)m
-1
N
This skeleton corresponds to a function f(x), whose derivative is
ƒ'(x) = a(x + 1)”(x − 1)™,
with
a = 1
v, n = 2, and m = 2 v
-1
This skeleton corresponds to a function f(x), whose derivative is
f'(x) = a(x + 1)" (x − 1)™,
with
a = -1, n = 2 ✓ and m
1
Transcribed Image Text:Consider the following graph of a derivative f':
(a) At what x-values do the points of inflection of f occur?
x = (2,5)
(Click on the graph to enlarge it)
(Enter your answer as a value, or a comma-separated list of values, or NONE.)
(b) On which interval(s) is f concave down?
f is concave down for x in (-1,1)
(Enter your answer using help (intervals).)
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