Question
Asked Nov 4, 2019
166 views
This exercise involves local maxima and minima of polynomial functions. A graphing calculator is recommended.
(a) Graph the function P(x) = (x - 4)(x - 5) (x - 6) and find all local extrema, correct to the nearest tenth
(х, у) %3D
local minimum
local maximum
(х, у) 3D
(b) Graph the function Q(x) = (x - 4)(x - 5)(x - 6) + 7 and use your answers to part (a) to find all local extrema, correct to the nearest tenth.
(х, у) %3D
local minimum
local maximum
(х, у) %3
help_outline

Image Transcriptionclose

This exercise involves local maxima and minima of polynomial functions. A graphing calculator is recommended. (a) Graph the function P(x) = (x - 4)(x - 5) (x - 6) and find all local extrema, correct to the nearest tenth (х, у) %3D local minimum local maximum (х, у) 3D (b) Graph the function Q(x) = (x - 4)(x - 5)(x - 6) + 7 and use your answers to part (a) to find all local extrema, correct to the nearest tenth. (х, у) %3D local minimum local maximum (х, у) %3

fullscreen
check_circle

Expert Answer

Step 1

Given, function is

help_outline

Image Transcriptionclose

P(x)(x-4)(x-5)(x-6) O(x)(x-4)(x-5)(x-6)+7

fullscreen
Step 2

Take function P(x) and find critical points,

Differentiate P(x) with respect to x,

help_outline

Image Transcriptionclose

P'(x)=(x-4)(x-5)(x-6) d =(x-4)(x-5)x-6)+(x-4)(x-6) (x-5)+(x-6)(x-5) -(x-4)(x-5)+(x-4)(x-6)+ (x- 6) (x-5) =x-9x+20+x-10x+24+x2- 11x+30 (x-4) =3x-30x+74

fullscreen
Step 3

For critical points, take deriv...

help_outline

Image Transcriptionclose

P'(x) 0 3x2-30x+74 0 30t-30)-4(3)(74) x=. 2(3) 30t900-888 x= 6 30+v12 6 30±23 x= 6 15-5 15+3 x= x= 5.6, x= 4.4

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in
MathCalculus

Derivative