Which of the following are given by
(a) The slope of the tangent when
(b) The y-coordinate of the point where
(c) The instantaneous rate of change of
(d) The marginal revenue at
Trending nowThis is a popular solution!
Chapter 9 Solutions
Mathematical Applications for the Management, Life, and Social Sciences
- , find the derivative of y with respect to the appropriate variable 21. y = ln cosh y - 1/2 tanh2 y 22. y = ln sinh y - 1/2 coth2 yarrow_forwardFind a function y=f(x) whose second derivative is y''=12x-2 at each point (x,y) on its graph y=-x+5 and is tangent to the graph at the point corresponding to x=-1 .arrow_forwardFind the derivative of the function y = x tanh−1 x + ln√(1 − x2)arrow_forward
- 1. Find the second derivative with respect to y ifarrow_forwardA ladder of length 9 meters is leaning against a vertical wall. Due to the smoothness of the ground, the foot of the ladder is sliding. Let y be the vertical distance of the top of the ladder from the ground and x be the horizontal distance of the foot of the ladder from the wall. If the rate of change of y with respect to x is numerically equal to -kx, find k when x = 1.1 meters.arrow_forwardA ladder 5 meters long is leaning against a vertical wall. Due to the smooth floor, the foot of the ladder is sliding away from the wall. Let x be the horizontal distance of the foot of the ladder from the wall and y be the height of the top of the ladder from the floor. Determine when will the rate of change of y with respect to x be numerically equal to the negative of the current value of x?arrow_forward
- The tangent line to the graph of y=f(x)at the point (1,11) has the equation y=3x+8 (a) Find f′(1) Find the instantaneous rate of change of y with respect to x at x=1.arrow_forwardDetermine the gradient of the straight line which is tangent to the graph of f(x)= tan^-1(ln x) at the point (1;0)arrow_forwardConcerning implicit differentiation, is the derivative of y equal to dy/dx?arrow_forward
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education