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Activity 2.5.4. Use known derivative rules, including the chain rule, as needed to answer each of the following questions. a. Find an equation for the tangent line to the curve y = Vex +3 at the point where x = 0. b. If s(t) = 1 represents the position function of a particle moving horizontally along an axis at time t (t2 + 1)3 (where s is measured in inches and t in seconds), find the particle's instantaneous velocity at t = 1. Is the particle moving to the left or right at that instant? c. At sea level, air pressure is 30 inches of mercury. At an altitude of h feet above sea level, the air pressure, P, in inches of mercury, is given by the function P = 30e-0.0000323h Compute dP/dh and explain what this derivative function tells you about air pressure, including a discussion of the units on dP/dh. In addition, determine how fast the air pressure is changing for a pilot of a small plane passing through an altitude of 1000 feet. d. Suppose that f(x) and g(x) are differentiable functions and that the following information about them is known: f(x) f'(x) g(x) g'(x) -1 2 -5 -3 4 -3 4 -1 Table 2.5.6: Data for functions f and g. If C(x) is a function given by the formula f(g(x)), determine C'(2). In addition, if D(x) is the function f(f(x)), find D'(-1).

Activity 2.5.4. Use known derivative rules, including the chain rule, as needed to answer each of the following questions. a. Find an equation for the tangent line to the curve y = Vex +3 at the point where x = 0. b. If s(t) = 1 represents the position function of a particle moving horizontally along an axis at time t (t2 + 1)3 (where s is measured in inches and t in seconds), find the particle's instantaneous velocity at t = 1. Is the particle moving to the left or right at that instant? c. At sea level, air pressure is 30 inches of mercury. At an altitude of h feet above sea level, the air pressure, P, in inches of mercury, is given by the function P = 30e-0.0000323h Compute dP/dh and explain what this derivative function tells you about air pressure, including a discussion of the units on dP/dh. In addition, determine how fast the air pressure is changing for a pilot of a small plane passing through an altitude of 1000 feet. d. Suppose that f(x) and g(x) are differentiable functions and that the following information about them is known: f(x) f'(x) g(x) g'(x) -1 2 -5 -3 4 -3 4 -1 Table 2.5.6: Data for functions f and g. If C(x) is a function given by the formula f(g(x)), determine C'(2). In addition, if D(x) is the function f(f(x)), find D'(-1).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Activity 2.5.4. Use known derivative rules, including the chain rule, as needed to answer each of the following questions. a. Find an equation for the tangent line to the curve y = ve* +3 at the point where x = 0. b. If s(t) = 1 represents the position function of a particle moving horizontally along an axis at time t (t2 + 1)3 (where s is measured in inches and t in seconds), find the particle's instantaneous velocity at t = 1. Is the particle moving to the left or right at that instant? c. At sea level, air pressure is 30 inches of mercury. At an altitude of h feet above sea level, the air pressure, P, in inches of mercury, is given by the function P = 30e-0.0000323h. Compute dP/dh and explain what this derivative function tells you about air pressure, including a discussion of the units on dP/dh. In addition, determine how fast the air pressure is changing for a pilot of a small plane passing through an altitude of 1000 feet. d. Suppose that f(x) and g(x) are differentiable functions and that the following information about them is known: f(x) f'(x) g(x) g'(x) -5 -1 -3 4 -3 4 -1 Table 2.5.6: Data for functions f and g. If C(x) is a function given by the formula f(g(x)), determine C'(2). In addition, if D(x) is the function f(f(x)), find D'(-1).
Transcribed Image Text:Activity 2.5.4. Use known derivative rules, including the chain rule, as needed to answer each of the following questions. a. Find an equation for the tangent line to the curve y = ve* +3 at the point where x = 0. b. If s(t) = 1 represents the position function of a particle moving horizontally along an axis at time t (t2 + 1)3 (where s is measured in inches and t in seconds), find the particle's instantaneous velocity at t = 1. Is the particle moving to the left or right at that instant? c. At sea level, air pressure is 30 inches of mercury. At an altitude of h feet above sea level, the air pressure, P, in inches of mercury, is given by the function P = 30e-0.0000323h. Compute dP/dh and explain what this derivative function tells you about air pressure, including a discussion of the units on dP/dh. In addition, determine how fast the air pressure is changing for a pilot of a small plane passing through an altitude of 1000 feet. d. Suppose that f(x) and g(x) are differentiable functions and that the following information about them is known: f(x) f'(x) g(x) g'(x) -5 -1 -3 4 -3 4 -1 Table 2.5.6: Data for functions f and g. If C(x) is a function given by the formula f(g(x)), determine C'(2). In addition, if D(x) is the function f(f(x)), find D'(-1).
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