Application of derivatives Questions and Answers

The region shaded in the diagram is rotated 360 around the x axis Find the volume in units cubed u of the three dimensional shape it creates 7 6 5 4 3 2 1 0 1 2 3 4 y 0 1 2 y x 3 4 X

4 lim 240 sin 22 7z 22 2 z z 1

Find a particular solution to the differential equation using the Method of Undetermined Coeffic x t 4x t 4x t 1212 e t A solution is x t

Prove that for every prime p and for all natural numbers a a ged p a p iff p divides a b ged p a 1 iff p does not divide a

5 The members of a youth football program are required to sell tickets to chicken dinners for the program s fundraiser They can sell adult tickets for 10 and child tickets for 5 Each athlete must bring in at least 350 from the ticket sales Write an expression to represent the total amount of money an athlete makes from ticket sales Let x represent the number of adult tickets sold and let y represent the number of child tickets sold Write an inequality in two variables to represent the amount an athlete must make Graph the inequality from part b Use the graph to determine whether an athlete will bring in at least 350 when they sell 10 adult tickets and 30 child tickets Explain your reasoning

Relative Maximum at x Where any relative maximum s relative minimum s and Horizontal Points of Inflection occur No Relative Maximum Relative Minimum at x O No Relative Minimum Inflection Point s at x No Inflection Point 2 2 increasing Use interval notation to identify where f x is

find the local maximum and minimum values and saddle points of the function a f x y x 2 xy y 2 y b f x y y e x 1

Find an equation of the tangent line to the graph of the function at the given point f x 1 x x 6 3 18 y 81 225

13 Find the volume of the solid obtained by rotating about the x axis the region enclosed by the curves y 9 x 9 y 0 x 0 and x 3

Find the average value of f x x 1 x 1 x 7

What are the zero s of the function f x 5x 2 25x x

The functions f x and g x are inverses f x involves the following operations in the following order Divide by 2 Add 5 Which operations must be part of g x Subtract 5 Multiply by 2 Multiply by 2 Add 5 Subtract 5 Multiply by 2 Add 5 Multiply by 2

Determine the value for c so that lim f x exists x 5 f x 2 x 9 for x 5 2 x c for x 5 The value of cis

rk 2 7 Deriva 0 11 answered n 10

Find the x values of all points whe f x x 3 6x 2 12x 1

OTK 2 7 De 0 11 answel ion 3