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1) Consider f(x) = 3x¹ − 8x³ +6 a) Find all critical points of the function (make sure to consider if the derivative is defined everywhere or not!). Label them in increasing order, 11, 12, 13, etc (for how many you find). b) Use the first derivative test to determine if x₁ is a local max, min, or neither. Find the y value associated with thisz value and write it as a point (x, y). 1 c) Use the second derivative test to determine if 7₂ is a local max, min, or neither. Find the y value associated with this z value and write it as a point (x, y).

1) Consider f(x) = 3x¹ − 8x³ +6 a) Find all critical points of the function (make sure to consider if the derivative is defined everywhere or not!). Label them in increasing order, 11, 12, 13, etc (for how many you find). b) Use the first derivative test to determine if x₁ is a local max, min, or neither. Find the y value associated with thisz value and write it as a point (x, y). 1 c) Use the second derivative test to determine if 7₂ is a local max, min, or neither. Find the y value associated with this z value and write it as a point (x, y).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1) Consider f(x) = 3x4 -8x³ +6 a) Find all critical points of the function (make sure to consider if the derivative is defined everywhere or not!). Label them in increasing order, 21, 22, 23, etc (for how many you find). b) Use the first derivative test to determine if x₁ is a local max, min, or neither. Find the y value associated with this a value and write it as a point (x, y). 1 c) Use the second derivative test to determine if x₂ is a local max, min, or neither. Find the y value associated with this a value and write it as a point (x, y).
Transcribed Image Text:1) Consider f(x) = 3x4 -8x³ +6 a) Find all critical points of the function (make sure to consider if the derivative is defined everywhere or not!). Label them in increasing order, 21, 22, 23, etc (for how many you find). b) Use the first derivative test to determine if x₁ is a local max, min, or neither. Find the y value associated with this a value and write it as a point (x, y). 1 c) Use the second derivative test to determine if x₂ is a local max, min, or neither. Find the y value associated with this a value and write it as a point (x, y).
d) Find all of the inflection points of the function. Make sure to test if they are inflection points or not! Find the y value(s) associated with the x value(s) and write as a point (x, y). 2 e) Use this knowledge of your function to sketch a fairly accurate graph. You may double-check with a calculator or graphing software, but you need to draw the graph by hand, and label each point that you found in the parts above as well as use the knowledge of where the function is increasing, decreasing, concave up, or concave down. y I
Transcribed Image Text:d) Find all of the inflection points of the function. Make sure to test if they are inflection points or not! Find the y value(s) associated with the x value(s) and write as a point (x, y). 2 e) Use this knowledge of your function to sketch a fairly accurate graph. You may double-check with a calculator or graphing software, but you need to draw the graph by hand, and label each point that you found in the parts above as well as use the knowledge of where the function is increasing, decreasing, concave up, or concave down. y I
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