0
answers
0
watching
176
views
11 Nov 2019
Investigate the family of curves defined by the parametric equations x =t2, y = t3 - ct, where c is a positive constant. Graph the curves for c = 1/4, c = 1 and c = 4.What features do all the curves have in common? (You may need to adjust the graphing window as you change c.) How does the shape change as c increases? Find the x- and y-coordinates of all points where the tangent line is horizontal or vertical. Verify that the point (c, 0) is on the curve for any c > 0.How many tangent line does the curve have at the point (c, 0)? What are their slopes? Check your answer numerically (for c = 1/4., c = 1 and c = 4) by drawing the tangent line on your graphing calculator. Consider the curve corresponding to c =1/3. Part of this curve is a loop. Find the length of that loop.
Investigate the family of curves defined by the parametric equations x =t2, y = t3 - ct, where c is a positive constant. Graph the curves for c = 1/4, c = 1 and c = 4.What features do all the curves have in common? (You may need to adjust the graphing window as you change c.) How does the shape change as c increases? Find the x- and y-coordinates of all points where the tangent line is horizontal or vertical. Verify that the point (c, 0) is on the curve for any c > 0.How many tangent line does the curve have at the point (c, 0)? What are their slopes? Check your answer numerically (for c = 1/4., c = 1 and c = 4) by drawing the tangent line on your graphing calculator. Consider the curve corresponding to c =1/3. Part of this curve is a loop. Find the length of that loop.