Semicubical Parabola Problem: A parametric function has the equations x = t 2 y = t 3 a

Chapter 4, Problem 4

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Semicubical Parabola Problem: A parametric function has the equations x = t 2 y = t 3 a. Make a table of values of x and y for each integer value of t from 3 through 3. b. Plot the graph of this function on graph paper, using the points found in part a. c. Find dy/dx when t = 1. Show that the line through the point (x, y) from part a, with slope dy/dx, is tangent to the graph at that point. d. Eliminate the parameter t. Find y in terms of x. From the result, state why this graph is called a semicubical parabola.e. Find dy/dx by direct differentiation of theequation in part d. Show that the value ofdy/dx calculated in this way is equal to thevalue you found in part c by using theparametric chain rule.