Find the slope of the tangent line to the ellipse x24 y29 1

Find the slope of the tangent line to the ellipse x2/4+ y2/9 = 1 at the point (x,y). slope = Are there any points where the slope is not defined? (Enter them as comma-separated ordered- pairs, e.g., (1,3), (-2,5). Enter none if there are no such points.) slope is undefined at

Solution

y=3sqrt(1-x^2/4) dy/dx=(3/2)(-x/2)/(sqrt(1-x^2/4)) =-3x/2sqrt(4-x^2) slope is not defined where x=2,-2 slope tends to infinity (2,0),(-2,0)