MTH130 Module 2 - Section Assignment 3.6 (Homework)

2.

Find dy by implicit differentiation. dx = 5x + 4y 2 dy = dxFollow the steps below for the given function. x3 - 4x2 - xy = 9 Solve the equation for y. Y= Differentiate this equation with respect to x. y' Complete the steps below to implicitly take the derivative of the original equation. (Leave your final answer in terms of x and y.) x5 - 4x- - xy = 9 -xy = 9 - x3 +4x2 d (-xy) = (9 ) d + 9 (4 x 2) dx dx dx dx d V) - y- (x) = 0 - 3x2+ dx dy = -3x2 + + y dx dy dxEffect of Price on Supply of Eggs Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related to the weekly supply x (in thousands of cartons) by the following equation. 625p2 - x2 =100 If 37000 cartons of eggs are available at the beginning of a certain week and the price is falling at the rate of 6c/carton/week, at what rate is the supply changing? (Round your answer to the nearest whole number.) (Hint: To find the value of p when x = 37, solve the supply equation for p when x = 37.) cartons per week