Basic Differentiation Rules and Rates of Change 2.2 121 105. Velocity Verify that the average velocity over the time interval [to velocity at t =to for the position function At, to Ar] is the same as the instantaneous s)2ar +c. 106. Inventory Management The annual inventory cost C for a manufacturer is 1,008,0006.3Q с. Q 1 where Q is the order size when the inventory is replenished. Find the change in annual cost when Q is increased from 350 to 351 and compare this with the instantaneous rate of change when Q = 350. 107. Finding an Equation of a Parabola Find an equation of the parabola y ax + bx + c that passes through (0, 1) and is tangent to the line y = x - 1 at (1,0). 108. Proof Let (a, b) be an arbitrary point on the graph of y 1/x, x> 0. Prove that the area of the triangle formed by the tangent line through (a, b) and the coordinate axes is 2. 109. Tangent Line Find the equation(s) of the tangent line(s) to the graph of the curve y = -9x through the point (1, -9) not on the graph. 110. Tangent Line Find the equation(s) of the tangent line(s) to the graph of the parabola y x through the given point not on the graph. (a) (0, a) (b) (a, 0)

Basic Differentiation Rules and Rates of Change 2.2 121 105. Velocity Verify that the average velocity over the time interval [to velocity at t =to for the position function At, to Ar] is the same as the instantaneous s)2ar +c. 106. Inventory Management The annual inventory cost C for a manufacturer is 1,008,0006.3Q с. Q 1 where Q is the order size when the inventory is replenished. Find the change in annual cost when Q is increased from 350 to 351 and compare this with the instantaneous rate of change when Q = 350. 107. Finding an Equation of a Parabola Find an equation of the parabola y ax + bx + c that passes through (0, 1) and is tangent to the line y = x - 1 at (1,0). 108. Proof Let (a, b) be an arbitrary point on the graph of y 1/x, x> 0. Prove that the area of the triangle formed by the tangent line through (a, b) and the coordinate axes is 2. 109. Tangent Line Find the equation(s) of the tangent line(s) to the graph of the curve y = -9x through the point (1, -9) not on the graph. 110. Tangent Line Find the equation(s) of the tangent line(s) to the graph of the parabola y x through the given point not on the graph. (a) (0, a) (b) (a, 0)

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Description: 106 Basic Differentiation Rules and Rates of Change2.2121105. Velocity Verify that the average velocity over the timeinterval [tovelocity at t =to for the position functionAt, toAr] is the same as the instantaneouss)2ar +c.106. Inventory Management T

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.6: Variation

Problem 31E

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