Homework 3.5

Question 1

The demand x is the number of items that can be sold at a price of $p. For x = a} 9,000 - p3 , nd the rate of change of p with respect to x by differentiating implicitly. The rate of change of the price p with respect to the demand x is :l. Use implicit differentiation to nd y' for the equation below and then evaluate y' at the indicated point. y2+2y+3x=0;(-5,3) FD y'|(_5,3) = Cl (Simplify your answer.) The graph of (x - 2)2 + (y -3)" = 1 is shown on the right. Use implicit differentiation to find the slopes of the tangent lines at the points on the graph where x = 2.6. Check your answers by visually estimating the slopes on the graph in the figure. Using implicit differentiation, the formula for y', the slope of the tangent lines, is.Find the equation(s) of the tangent line(s) to the graph of the indicated equation at the point(s) with the given value of x. xy - 2x - 16 = 0; X = 4 . . . Find the equation(s) of the tangent line(s) to the graph of the given equation at x = 4. (Type an equation. Use a comma to separate answers as needed.)