Curve #2 Product rule Given the curve 4x2 + xy + 10 =5x+6 a. Find the derivative. Show all work. 48x 1 8 x + ( 10 ( y )+ xax = 5 xx - x -1 dx = 5 - y - 8x cy - 5 - y - 8x X X X dx en! b. Find all points on the curve where the x-value is 2. Show all work. * = z 2 4 24 12014 ( 2 ) 2 + 2 (2) + 10 = 5 dx c. Find the derivative at the point from part b. d. Write the equation of the tangent line using your point in part b and your slope in part c. e. Write the equation of the normal line using your point from part b. f. On a second Desmos tab, graph the given curve, the point on the curve in part b, the equation of the tangent line in part d, and the equation of the normal line in part e. "Curve #3 Given the curve x' + 3xy -4x = 2+4yz a. Find the derivative. Show all work. b. Find all points on the curve where the y-value is 1. Show all work. *note: there should be more than one point! c. Find the derivative at EACH point from part b. Point 1: Point 2: Work for slope at point 1: Work for slope at point 2: d. Write the equation of the tangent lines using your points in part b and your slopes in part c. Point 1: Point 2: Equation of the tangent line at Point 1: Equation of the tangent line at Point 2: e. Write the equations of the normal lines using your point from part b. Point 1: Point 2: Equation of the normal line at Point 1: Equation of the normal line at Point 2: a. On a third Desmos tab, graph the given curve, the points on the curve in part b, the equation of the tangent lines in part d, and the equation of the normal lines in part e.Curve #4 Given the curve x2 -6y +9 =4x- >2 a. Find the derivative. Show all work. b. How do you find the points where a curve has horizontal tangent lines? c. Find the POINTS (you need an x-value and y-value) where the curve has horizontal tangent lines. d. Write the equation of the tangent lines at both points where the curve has horizontal tangent lines. e. How do you find the points where a curve has vertical tangent lines? f. Find the POINTS (x and y) where the curve has vertical tangent lines. g. Write the equation of the tangent lines at both points where the curve has vertical tangent lines. g. On a fourth Desmos tab, graph the given curve, the points on the curve in part c, the tangent lines in part d, the points in part f, and the equation of the tangent lines in part g