Daily Challenge 1 Please solve the following st

Daily Challenge 1. Please solve the following: s(t) = at 2 + bt + c, so using s ‘(t) =previous v(t) = 2 atresults +b But =at ½gt s(t) t =20, + v(0)t v(0) += c, b, so but s(0) v(t) == 02 at = c+ v(0) Or letting s(t) = ½gt g 2=+2 a v(0)t since a(t) = v’(t) = 2 a, then v(t) = gt + v(0) Jim Napolitano: BSGE HS DP Math

Questions, Questions 1. Essential Question: How can the Calculus solve real world problems? 2. Guiding Question: How are the behaviors of curves communicated analyzed? Jim Napolitano: BSGE HS DP Math

Homework Review • “Problem” homework problems: 22 D. 1 p 565 #2 22 D. 2 p 570 #2 - 4 Jim Napolitano: BSGE HS DP Math

Mini-Lesson 1. Curve Properties: You Can Understand Math Text! • Recall the first derivative is a slope function, Monotonic functions arethe functions that tend to move i. e. : it tells us slope of the tangent to in a only one direction asat x increases. curve any point. A monotonic increasing function always increases as x increases, i. e. f(a)>f(b) for all • monotonic That slope (or derivative sign) tellsdecreases us whether a>b. A decreasing function always as x is increasing orcalculus decreasing increases, the i. e. curve f(a)<f(b) for all a>b. In speak, a monotonic decreasing function's derivative is always • The textbookincreasing uses the term monotonicity negative. A monotonic function's derivativetois describe increasing or decreasing behavior for always positive… all x. What does this mean? Did you research the Because it is term? uncommon to find functions which strictly increase or strictly decrease, we sometimes call a function monotonic on a restricted domain. For instance, cos(x) is monotonic decreasing within 0<x< . Jim Napolitano: BSGE HS DP Math http: //library. thinkquest. org/2647/algebra/ftmonoto. htm

Mini-Lesson 1. Curve Properties (Continued): • Recall how to define curve intervals: Jim Napolitano: BSGE HS DP Math

Mini-Lesson 1. Curve Intervals (Continued): So for increasing/decreasing intervals: Jim Napolitano: BSGE HS DP Math

Mini-Lesson 2. Curve Properties - Example: Jim Napolitano: BSGE HS DP Math

Mini-Lesson 3. Sign Diagrams: Jim Napolitano: BSGE HS DP Math

Mini-Lesson 4. Sign Diagrams – Examples: Jim Napolitano: BSGE HS DP Math

Group Work 1. Please solve the following: Jim Napolitano: BSGE HS DP Math

Homework • Textbook: – Please read 22 E p 571 – 578 • Please do exercises: 22 E. 1 p 573 #1 22 E. 2 p 574 #2 bc, 3 a • Journal: – Please answer the Guiding Question. Jim Napolitano: BSGE HS DP Math