9) (1) Consider the function (a) Find all critical points of the function. (b) Use part (a) to find all local max/min points of the function. (c) State where the function is increasing / decreasing. f(x) = x² - 4x³ (d) Find all points of inflection (e) State where the function is concave up/ concave down. (f) Sketch a graph of this function. Be sure to label all intercepts, local mins/maxes, inflection points. F(X)= X4-4X³

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter5: Graphs And The Derivative
Section5.1: Increasing And Decreasing Functions
Problem 22E
icon
Related questions
Question
Do each part
a)
(1) Consider the function
f(x) = x² - 4x³
(a) Find all critical points of the function.
(b) Use part (a) to find all local max/min points of the function.
(c) State where the function is increasing / decreasing.
(d) Find all points of inflection
(e) State where the function is concave up/ concave down.
(f) Sketch a graph of this function. Be sure to label all intercepts, local mins/maxes,
inflection points.
F(X)= X4-4x³
Transcribed Image Text:a) (1) Consider the function f(x) = x² - 4x³ (a) Find all critical points of the function. (b) Use part (a) to find all local max/min points of the function. (c) State where the function is increasing / decreasing. (d) Find all points of inflection (e) State where the function is concave up/ concave down. (f) Sketch a graph of this function. Be sure to label all intercepts, local mins/maxes, inflection points. F(X)= X4-4x³
Expert Solution
steps

Step by step

Solved in 7 steps with 7 images

Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage