Use a graphing utility to graph the curve represented by the parametric equations x = t2 − t + 2, y = t3 − 3t , (a) use a graphing utility to find dx/dt, dy/dt, and dy/dx at the given value of the parameter t = −1, (b) find an equation of the tangent line to the curve at the given value of the parameter, and (c) use a graphing utility to graph the curve and the tangent line from part (b)

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5: A potato cannon launches a potato straight up from a height of 5 feet with an initial velocity of 128 ft/sec. The horizontal distance from the cannon launch and the vertical height from the ground, in feet, are modeled by a set of parametric equations. . Write a set of parametric equations that will model the height of the potato as a function of time, t. . Find the average rate of change in horizontal position over the first two seconds. Show your work and units. What is the average rate of change in vertical motion over the first two seconds? Show your work and units.

Find parametric equations for the line tangent to the curve of intersection of the surfaces at the given point. x = 1 Surfaces: x + y² + 2z = 4, Point: (1,1,1) Find the equations for the tangent line. Let z = 1-2t. X = =(Type an expression using t as the variable.)