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Concavity & inflection point

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Presentation on theme: "Concavity & inflection point"— Presentation transcript:

1 Concavity & inflection point
Subject 143 141 131 132 Delta-epsilon 1 Continuity 2 Find f’ 4 6 7 Related rate Limit 3 others 1acce L’H MVT Anti-derivative Newton’s Optimization Increasing Max & Min Critical points Linear approximation Concavity & inflection point Asymptotes

2 3.6 Log Diff 3.4 Chain Rule 3.1 Poly&exp 3.5 Implicit Diff
Differentiation 3.6 Log Diff variables appear in the base and exponent 3.4 Chain Rule 3.1 Poly&exp 3.5 Implicit Diff Implicit Diff 3.2 Prod&Quo 3.11 Hyp 3.3 Trig 3.5 Inv. Trig The slope of the tangent line to the curve An equation of the normal line An equation of the tangent line The slope of the normal line to the curve Types of Q

3 Differentiation F143 F122 F141 INVERSE TRIGONOMETRIC FUNCTIONS
HYPERBOLIC FUNCTIONS F122 F141 LOGARITHMIC & Exponential Chain Rule Implicit Differentiation

4 ANTIDIFFERENTIATION F141 F143 F122

5 Limit and L’H number 1 Evaluate Number/0 1) 2) 3) 4) 2 squeeze

6 Limit and L’H F083 121 F143

7 Continuity F141 F132 F151

8 Five theorems 1)Newton’s method 2)Roll’s thm 3)MVT 4)EVT 5)IVT

9 First derivative f’(x) second derivative f’’(x)
1)Critical points 2)Increasing and decreasing 3)local Max,Min 1)Inflection points 2)Concave up and down 3)Local Max,Min domain domain Max Min Max Min

10 1) Newton’s method

11 2)Critical Points Find Domain First

12 3)Absolute Max,Min (M,m)

13 4)local Max,Min

14 5)Increasing, Decreasing

15 6)Concave, up-down f cont at c

16 7)Inflection points

17 8)Maximize or Minimize(WE1)
I) What Max or min A =area V=volume P=product III)1variable A =area V=volume P=product II) EquationWrite A =area V=volume P=product

18 9)MeanValue or Rolle’s

19 10) Anti-drivative

20 11) L’Hospital 1)common denominator, or 2)rationalization (conjugate)
3)common factor

21 12) Linear Approximation

22 13) Memorize

23 Multiple choice Exam 1) Skim all 28 problems to select these you know then mark them Look for the keyword: local , inc, concave, inflection, Newton,….. 2) Start by solving these problems (keep bubbling at the end) you have 180min/28Prob = 6.4min each 3) Eliminate answers that are wrong 4) Try working backwards. Plug the answers into the question to see if they make sense

24 Multiple choice Exam 4) If you have absolutely no idea what the answer is, can't use any of the above techniques, choose one letter 1) Pattern: Look for similarities V1 V2 V3 V4 A 6 4 5 B 7 3 8 C 9 D E

25 Multiple choice Exam V1 V2 V3 V4 A 9 7 6 B 2 5 4 C 8 D E

26 Use your knowledge in Graph

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