Question

8) Find the points (x,y) on the curve given by x = 1+t2 and y=t-t3 where the tangent line is horizontal. Graph the curve and locate these points. Provide scales on both axes. Suggestion: On Desmos, let-2 st s 2 to see the full curve and to estimate where these points are. Points

Answer 1

given that, & y = t-t3 (1) Let's diffeentrate the given equations. aut de 0+ 2t dt da at = 2t. > du BEN at Now, بیان dy at da dai alt 1-3tr at we know that, for the houzontal tangent line. dy da 1-3tu at t = t u

let usfind ay vales by using t value (t = 1) When t= V then we get the os a vale 3 the Y vale au y = 2 303 니 T. (14) 2 3/3 when, 7/3 Similarly 19,43 = ( )

N -1- (1/3333, 0.385) 2 3 (1.3333, -0.385) -2

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