Calculus:

1.

Consider the fol owing problem: Find two numbers whose sum is 23 and whose product is a maximum. (a) Complete the table of values so that the sum of the numbers in the first two columns is always 23. First number Second number Product 1 22 22 2 21 42 3 20 On the basis of the evidence in the table, estimate the answer to the problem. (Enter your answers as a comma-separated list.) : (b) Use calculus to solve the problem. (Enter your answers as a comma-separated list.) : Consider the equation below. f(x) = 7 sin(x) + 7 cos(x), 0 S x S 2:: (a) Find the interval on which fis increasing. (Enter your answer using interval notation.) (b) Find the local minimum and maximum values of f. local minimum value 7\\/ 2 J local maximum value 7V 2 J (c) Find the inflection points. (x, y) = (|:| X )(smallerxvalue) (X, y) = ( I X )(larger x-value) Find the interval on which f is concave up. (Enter your answer using interval notation.) 5. [-/0.06 Points] DETAILS SESSCALC2 3.5.011.MI. MY NOTES ASK YOUR TE If 1,200 cm of material is available to make a box with a square base and an open top, find the largest possible volume of the box. cm Need Help? Read It Watch It Master It 6. [-/0.06 Points] DETAILS SESSCALC2 3.5.014. MY NOTES ASK YOUR TE A rectangular storage container with an open top is to have a volume of 10 ms. The length of this base is twice the width. Material for the base costs $5 per square meter. Material for the sides costs $3 per square m cheapest such container. (Round your answer to the nearest cent.) $ Need Help? Read It 7. [-/0.1 Points] DETAILS SESSCALC2 3.5.040. MY NOTES ASK YOUR TE At which points on the curve y = 1 + 60x3 - 2x does the tangent line have the largest slope? ( x, y ) = (smaller x-value) ( x, y ) = ( (larger x-value) Need Help? Read It 8. [-/0.1 Points] DETAILS SESSCALC2 3.5.045. MY NOTES ASK YOUR TEA A baseball team plays in a stadium that holds 53,000 spectators. With ticket prices at $10, the average attendance had been 49,000. When ticket prices were lowered to $8, the average attendance rose to 51,000. (a) Find the demand function (price p as a function of attendance x), assuming it to be linear. P (x) = (b) How should ticket prices be set to maximize revenue? (Round your answer to the nearest cent.) $ Need Help? Read It Watch It