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11X1 T12 02 critical points (2010)
- 3. Critical Points
dy
Critical points occur when 0 or is undefined
dx
y
x
- 4. Critical Points
dy
Critical points occur when 0 or is undefined
dx
y
x
- 5. Critical Points
dy
Critical points occur when 0 or is undefined
dx
f x 0, maximum turning point
y
x
- 6. Critical Points
dy
Critical points occur when 0 or is undefined
dx
f x 0, maximum turning point
y
x
f x 0, minimum turning point
- 9. y
f x 0, horizontal point of inflection
x
- 10. y
f x 0, horizontal point of inflection
x
y
x
- 11. y
f x 0, horizontal point of inflection
x
y
x
f x is undefined, vertical tangent
- 14. y
x
f x is undefined, " cusp" curve is not continuous
minimum point
- 15. y
x
f x is undefined, " cusp" curve is not continuous
minimum point
Exercise 10C; 1, 2ace etc, 3, 5, 8, 10