The body mass index (BMI) of a person is defined by B ( m , h ) = m h 2 where m is the person’s mass (in kilograms) and h is the height (in meters). Draw the level curves B ( m , h ) = 18.5, B ( m , h ) = 25, B ( m , h ) = 30, and B ( m , h ) = 40. A rough guideline is that a person is underweight if the BMI is less than 18.5; optimal if the BMI lies between 18.5 and 25; overweight if the BMI lies between 25 and 30; and obese if the BMI exceeds 30. Shade the region corresponding to optimal BMI. Does someone who weighs 62 kg and is 152 cm tall fall into this category?
The body mass index (BMI) of a person is defined by B ( m , h ) = m h 2 where m is the person’s mass (in kilograms) and h is the height (in meters). Draw the level curves B ( m , h ) = 18.5, B ( m , h ) = 25, B ( m , h ) = 30, and B ( m , h ) = 40. A rough guideline is that a person is underweight if the BMI is less than 18.5; optimal if the BMI lies between 18.5 and 25; overweight if the BMI lies between 25 and 30; and obese if the BMI exceeds 30. Shade the region corresponding to optimal BMI. Does someone who weighs 62 kg and is 152 cm tall fall into this category?
The body mass index (BMI) of a person is defined by
B
(
m
,
h
)
=
m
h
2
where m is the person’s mass (in kilograms) and h is the height (in meters). Draw the level curves B(m, h) = 18.5, B(m, h) = 25, B(m, h) = 30, and B(m, h) = 40. A rough guideline is that a person is underweight if the BMI is less than
18.5; optimal if the BMI lies between 18.5 and 25; overweight if the BMI lies between 25 and 30; and obese if the BMI exceeds 30. Shade the region corresponding to optimal BMI. Does someone who weighs 62 kg and is 152 cm tall fall into this category?
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).
Does the series converge or diverge
Chapter 14 Solutions
Bundle: Calculus: Early Transcendentals, Loose-Leaf Version, 8th + WebAssign Printed Access Card for Stewart's Calculus: Early Transcendentals, 8th Edition, Multi-Term
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