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MAT 1221 Survey of Calculus Section 3.1 Increasing and Decreasing Functions

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Presentation on theme: "MAT 1221 Survey of Calculus Section 3.1 Increasing and Decreasing Functions"— Presentation transcript:

1 MAT 1221 Survey of Calculus Section 3.1 Increasing and Decreasing Functions

2 HW WebAssign HW 3.1 Additional HW listed at the end of the handout (need to finish, but no need to turn in) Please do your HW ASAP. Do not wait for Tuesday to do your HW. Read 3.2 for tomorrow.

3 Tutoring Bonus-Bonus Points 5 points for tutoring in the tutoring room 5 additional points from Caylee

4 Max/Min We are interested in max/min values Minimize the production cost Maximize the profit Maximize the sunlight exposure of plants

5 Preview Define increasing/Decreasing Function Increasing/Decreasing Test

6 Increasing/ Decreasing Functions x y t s

7 Increasing/ Decreasing Test

8 x y a b

9 x y a b

10 x y a b

11 x y a b

12 How to find the intervals of increasing and decreasing? x y a c b >0 =0 <0

13 Critical Number

14

15 Increasing/ Decreasing Test x y a c b >0 =0 <0

16 Increasing/ Decreasing Test The critical numbers divided the interval into subintervals. x a c b

17 x Increasing/ Decreasing Test a c b

18 Example 1 Find the intervals of increasing and decreasing of

19 Example 1 1. Find the critical numbers

20 Example 1 2. Sketch a diagram of the subintervals formed by the critical numbers

21 Example 1

22 Expected Solution Steps


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