from part (b) and solve for the x-values when f′′(x) = 24x^2 + 12 = 0. So, x = and x = − . To determine the y-coordinates for these points of inflection, determine f(x) at each of
these points: f = and f = . So the points of inflection occur at and .- Consider the curve given by x^3 y^2 − 5x + y = 3.
(a) Find .Use implicit differentiation: 2x^3 y + 3x^2 y^2 − 5 + = 0. Simplify and isolate : = .
(b) Find .Use the derivative from part (a) and differentiate again using implicit differentiation: = . Replace the value for from part (a) for the final
solution:No need to simplify.(c) Find the equation of the normal lines at each of the two points on the curve whose x-
coordinate is −1.From the original equation, at x = −1, y = −2 or y = 1. Plug those values into from part (a)