University:
Camosun College
Course:
NURS132 | Promoting Health and Wellbeing
Academic year:

2024
Views:

73

Pages:

4
Author:

Aysha A.

LAB INCREASING AND DECREASING FUNCTION'S AIM: To explore increasing and decreasing functions geometrically Concepts. • Increasing and decreasing function • Derivative of a function and slope of tangent at a point on a curve Activity 27.1 Increasing and Decreasing Procedure: Function I • Draw the graph of the function f(x)= • create a Slider a with Min = -5 and 4 Max =B plot the point A (a, Pla)) and B (Difca). Join AB. Gradually change the value of the Slide from 5 to 5 observe the movement of the point B. 9. Describe the motion of B as a increasing from 0 to 0. From 0 to -11B is moving uprocerds Kom-1 to 2 B is moving downcwards From 2 to do B 1) moving upwards. Q. Find the intervals in which the function fis strictly increasmagt smictly decreasing Answer. on (-001-1) POD 13 Strictly increasing On On (112) PCX) is Strictly cleereasing. on (200) Fex) is Strictly increasing Q. Observe the graph of the following functions and find the intervals in which they are Strictly increasing / Strictly detressing (You can doit bu by observation of the graph. In the graph the case of trignometne function change the markings on & aχίζ In term of x). 1. 22-21x16 2. Sinza cosx XEED] 3. x³-3x214 Answu: DFunction 13 shictly decreasing on (-80012) and Strictly increasing on (2,00). 2. Tunction 13 strictly increasing on (○) and (2^) and strictly decreasingon (쥭,쥬). 3. Function is always increasing Activity 27.2 increasing and demasing Functions-2 Procedure: Draw the graph of the function dise ussed in the above activity • create 0 a slider a and plot A (af (a)) Draw the tangent to the wive at A and find it slope. Q Pind the intervals in Which the slope of the teringent is positive / negective Answer: on (-20,0) Blope is negative On (0100) Slope is negative Therefore, fex)-'s a decreasing function CAMITLLA KOOTTAVMA MALARDLIRAM 9. Find the relation between the sign of fox) and the interval in which the funtion. fis Storictly increating Istrictly decreasing Answu: fcx) is positive, then function 13 Strictly Increasing fcx fax) 1) negatiul, then function is strictly decreasing. Activity 27.3 Increasing and decreasing Prodecure. Function-3 • Draw the graph of the function fex)=8x39 (cx)= 823-9x15x • Dhaw the graph of fosx) • plot the point at which the graph fcx7 melt Inx-x13. Show the coordinates of thex points. 'Q. find the intervals in which the function • Storetly increasing / Shictly clecrecusing Answe on (-2010.5) and (1.25,00) f(x) is Spictly increasing On (-0.5,1.25). Pox) is Strictly decreasing