f(x)=x^3+4.5x^2−12x+3 a) Determine the intervals on which f is concave up and concave down.f is concave up on: f is concave down on:  b) Based on your answer to part (a), determine the inflection points of f. Each point should be entered as an ordered pair (that is, in the form (x,y)).= c) Find the critical numbers of f and use the Second Derivative Test, when possible, to determine the relative extrema. List only the x-coordinates. Relative maxima at=Relative minima at= d) Find the x-value(s) where f′(x) has a relative maximum or minimum.f′ has relative maxima at:  f′ has relative minima at:

College Algebra (MindTap Course List)
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ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
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f(x)=x^3+4.5x^2−12x+3

a) Determine the intervals on which f is concave up and concave down.
f is concave up on: 
f is concave down on: 

b) Based on your answer to part (a), determine the inflection points of f. Each point should be entered as an ordered pair (that is, in the form (x,y)).
=

c) Find the critical numbers of f and use the Second Derivative Test, when possible, to determine the relative extrema. List only the x-coordinates.

Relative maxima at=
Relative minima at=

d) Find the x-value(s) where f′(x) has a relative maximum or minimum.
f′ has relative maxima at:  
f′ has relative minima at:  

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