A fitness instructor wants to mix two brands of protein powder to form a blend that limits the amount of fat and carbohydrate but maximizes the amount of fiber. The nutritional information is given in the table for a single scoop of protein powder. Suppose that the fitness instructor wants to make at most 180 scoops of the mixture. She also wants to limit the amount of fat to 480 g and she wants to limit the amount of carbohydrate to 696 g . a. Determine the number of scoops of each type of powder that will maximum the amount of fiber. b. What is the maximum amount of fiber? c. If the fiber content were reversed between the two brands (that is, 8 g for brand A and 10 g for brand B ), then how much of each type of protein powder should be used to maximize the amount of fiber?
A fitness instructor wants to mix two brands of protein powder to form a blend that limits the amount of fat and carbohydrate but maximizes the amount of fiber. The nutritional information is given in the table for a single scoop of protein powder. Suppose that the fitness instructor wants to make at most 180 scoops of the mixture. She also wants to limit the amount of fat to 480 g and she wants to limit the amount of carbohydrate to 696 g . a. Determine the number of scoops of each type of powder that will maximum the amount of fiber. b. What is the maximum amount of fiber? c. If the fiber content were reversed between the two brands (that is, 8 g for brand A and 10 g for brand B ), then how much of each type of protein powder should be used to maximize the amount of fiber?
Solution Summary: The author calculates the number of scoops of each type of powder that will maximize the amount of fiber.
A fitness instructor wants to mix two brands of protein powder to form a blend that limits the amount of fat and carbohydrate but maximizes the amount of fiber. The nutritional information is given in the table for a single scoop of protein powder.
Suppose that the fitness instructor wants to make at most
180
scoops of the mixture. She also wants to limit the amount of fat to
480
g
and she wants to limit the amount of carbohydrate to
696
g
.
a. Determine the number of scoops of each type of powder that will maximum the amount of fiber.
b. What is the maximum amount of fiber?
c. If the fiber content were reversed between the two brands (that is,
8
g
for brand
A
and
10
g
for brand
B
), then how much of each type of protein powder should be used to maximize the amount of fiber?
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
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