AVERAGE RATE OF CHANGE AND SLOPE FOR PARAMETRIC EQUATIONS

Video Lesson

Solved Problems

Problem 1 :

For the particle whose position is determined by the equations

over the given interval -1 ≤ t ≤ 1, find the following.

(i) The average rate of change for x(t).

(ii) The average rate of change for y(t).

(iii) The slope of the graph between the points on the curve corresponding to t = -1 and t = 1.

Solution :

(i) The average rate of change for x(t) :

(ii) The average rate of change for y(t) :

(iii) The slope of the graph :

Problem 2 :

x = 3t

y = 3t² - 1

For the above parametric equations, over the given interval 0 ≤ t ≤ 2, find the following.

(i) The average rate of change for x(t).

(ii) The average rate of change for y(t).

(iii) The slope of the graph between the points on the curve corresponding to t = 0 and t = 2.

Solution :

(i) The average rate of change for x(t) :

(ii) The average rate of change for y(t) :

(iii) The slope of the graph :

Problem 3 :

x = 2(t - sin t)

y = 2(1 - cos t)

For the above parametric equations, over the given interval 0≤ t ≤ 2π, find the following.

(i) The average rate of change for x(t).

(ii) The average rate of change for y(t).

(iii) The slope of the graph between the points on the curve corresponding to t = 0 and t = 2π.

Solution :

(i) The average rate of change for x(t) :

(ii) The average rate of change for y(t) :

(iii) The slope of the graph :

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