Types of Stationary Points 2.2 Geometrical Application of Calculus 1. Minimum - - - - - - - 0 + + +...
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Transcript of Types of Stationary Points 2.2 Geometrical Application of Calculus 1. Minimum - - - - - - - 0 + + +...
![Page 1: Types of Stationary Points 2.2 Geometrical Application of Calculus 1. Minimum - - - - - - - 0 + + + + + + + xLHSMinimumRHS f’(x)< 0= 0> 0.](https://reader036.fdocuments.us/reader036/viewer/2022082506/5697bf8a1a28abf838c8aaac/html5/thumbnails/1.jpg)
Types of Stationary Points
2.2 Geometrical Application of Calculus
1. Minimum
---- - - - 0 ++
++
+++
x LHS Minimum RHS
f’(x) < 0 = 0 > 0
![Page 2: Types of Stationary Points 2.2 Geometrical Application of Calculus 1. Minimum - - - - - - - 0 + + + + + + + xLHSMinimumRHS f’(x)< 0= 0> 0.](https://reader036.fdocuments.us/reader036/viewer/2022082506/5697bf8a1a28abf838c8aaac/html5/thumbnails/2.jpg)
Types of Stationary Points
2.2 Geometrical Application of Calculus
2. Maximum
x LHS Maximum RHS
f’(x) > 0 = 0 < 0
++
+++ 0 - - ---
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![Page 3: Types of Stationary Points 2.2 Geometrical Application of Calculus 1. Minimum - - - - - - - 0 + + + + + + + xLHSMinimumRHS f’(x)< 0= 0> 0.](https://reader036.fdocuments.us/reader036/viewer/2022082506/5697bf8a1a28abf838c8aaac/html5/thumbnails/3.jpg)
Types of Stationary Points
2.2 Geometrical Application of Calculus
3.Point ofHorizontalInflection
x LHS Inflection RHS
f’(x) > 0 0 > 0
f’(x) < 0 0 < 0
+++
+ 0 ++++ ----- - 0 - ----
![Page 4: Types of Stationary Points 2.2 Geometrical Application of Calculus 1. Minimum - - - - - - - 0 + + + + + + + xLHSMinimumRHS f’(x)< 0= 0> 0.](https://reader036.fdocuments.us/reader036/viewer/2022082506/5697bf8a1a28abf838c8aaac/html5/thumbnails/4.jpg)
Types of Stationary Points
2.2 Geometrical Application of Calculus
1. Find any stationary points on the curve f(x) = x2 - 2x & determine what type it is.f’(x) = 2x - 2
2x - 2 = 0 (Stationary)2x = 2
f(1) = (1)2 – 2(1) = -1
LHS x = 0 Stationary x = 1 RHS x = 2
- 0 +
f’(0) = 2(0) - 2 = -2f’(2) = 2(2) - 2 = +2
(1, -1) is a Minimum
Stationary @ (1, -1)
x = 1
![Page 5: Types of Stationary Points 2.2 Geometrical Application of Calculus 1. Minimum - - - - - - - 0 + + + + + + + xLHSMinimumRHS f’(x)< 0= 0> 0.](https://reader036.fdocuments.us/reader036/viewer/2022082506/5697bf8a1a28abf838c8aaac/html5/thumbnails/5.jpg)
Types of Stationary Points
2.2 Geometrical Application of Calculus
2. Find the turning point on the curve y = 2x3 + 2 and determine what type it is.
f(x) = 2x3 + 2f’(x) = 6x2
6x2 = 0 (Stationary)x = 0
f(0) = 2(0)3 + 2 = 2
LHS x = -1 Stationary x = 0 RHS x = 1
+ 0 +
f’(-1) = 6(-1)2 = +6
f’(1) = 6(1)2 = +6
(0, 2) is a horizontal point of inflection
Stationary @ (0, 2)