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

2024
Views:

198

Pages:

5
Author:

Aysha A.

LAB-30 MAXIMA AND MINIMA him: To explore the concept alf local maxima and local minima to find pomt at local maximal, loced minima, absolute maximum geometrically Concepts: • local maxima and local minima • Absolute maximas and absolute minima Activity 30.1: Local marxima and Local minima First derivative test. X= C is a point of local maxima If fox) changes, sign from the 18-ve as * increases through c X= & 13 neither a poin I of local maxima nor a Point of local minima if f'cx) doesnol change sign as x C. increase through Second derivation test? KEL IS A POINA (ocal maxima if Pc)=0 and f"(c)<0 10 2°C is a local minima the best fallet Places if f'(c)=0 and Plex)>01 Procedure?. Q: Find the point of local. Maxima and local minima of the function f(x)-9x3-33x²+36x-8 Also find local maxima and local Minimum values. Inst Derivative test: Draw the graph of fex) and f'(x) find the Point A and B at which the graph f'(x) cuts the x-axis show the Coordinate of A and B • From the graph of f(x) it is easy to identify whether the x-coordinates of A and B are points of local maximat or local minima. • The input commands f(x(A)) and : f(x(B)) gives the correspond valles ames: local maximum at x : 0.75 local maximum value 3.81 local mimimum at x :2 Incol minimum value: -4. • Draw th graph of fox) and fox) and fa) • find the point A and B al which the graph uf f'(x) cuts the x coordmates of A and B. bers show the find the sign al 1"(x(A)) and fex(B)) f'(x(A)) = -30, x=0.75 is a local maximun f(x(B))=302= 2 is local minimum. 9. Find the point of local masuma and local minima of the function Isib (2x)31 Also find the local maximam and local minimum values. Procedure: • Create an integer slider n and marke the distance onx axisas 쥬 Draw the graphs of the Rivetioss.. fox)= 1 Sim (2x)1 and fas Identify the points at eulich either fex) is hot clifferentiable or f'(x)=0 maxima and • Imd point of local maxime local minima an local maxima atx= 3 7 local maximum value = 1 lo call minimum it.x= 2 local minimum valle: O Q. Find the ports of local maxim and local minimer of the following function also find the local maximum cond local minimum valles ans 9x112x+2, Activity 30.2 Absolute mau mum and absolute minimum 9. Find absolute maximum value and absolute minimum value of the following function in the given intervals 1. POD = 2x²-15x²+ 36x+1 in [1.5 Procedure: using the Input command cderivative + 36x+D draw. 15x2 the graph of f'(x) Find the points a bove graph meet/ A and B at which x-axis • Find FCID. FCS), fice CAD and f(x(8) Hig West among them is the absdute maximum value end least is the absolute meoximum value and least is the absomte value Ans. fcs) B6 f(x(A)) = 29and. PCX (B)) = 28 Absolute maximum 56 Absolute minimum > 25.