Stationary Points

Exercises for students
Solve the following problems and check your working using the above applet:

Find the coordinates of the turning points on the curve y = x³ - 2x² - 4x + 3. Use
(i) the first derivative test
(ii) the second derivative test
to determine the nature of each turning point. Sketch the curve.

Find the coordinates of the turning points on the curve y = x³ + 3. Use
(i) the first derivative test
(ii) the second derivative test
to determine the nature of each turning point. Sketch the curve.

Find the coordinates of the turning point on the curve y = - 2x² - 4x + 3. Use
(i) the first derivative test
(ii) the second derivative test
to determine the nature of the turning point. Sketch the curve.

Find the coordinates of the turning points on the curve y = x³ + 2x² - 4x - 5, stating the nature of each turning point.

Find the coordinates of the turning points of the curve y = x³ - x.



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