# Application of derivatives Questions and Answers

Calculus

Application of derivativesThe 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

Calculus

Application of derivativesFind 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

Calculus

Application of derivativesProve 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

Calculus

Application of derivatives5 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

Calculus

Application of derivativesRelative 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

Calculus

Application of derivativesfind 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

Calculus

Application of derivativesFind 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

Calculus

Application of derivatives13 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

Calculus

Application of derivativesThe 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

Calculus

Application of derivativesDetermine 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