Sketch the graph of the function f(x) = - x^3 + 3x^2 – 7. List the coordinated of where extrema or points of inflection occur. State where the function is increasing or decreasing as well as where it is concave up or concave down.

Isa Trevino

Isa Trevino

Answered question

2021-01-02

Sketch the graph of the function f(x)=x3+3x27. List the coordinated of where extrema or points of inflection occur. State where the function is increasing or decreasing as well as where it is concave up or concave down.

Answer & Explanation

BleabyinfibiaG

BleabyinfibiaG

Skilled2021-01-03Added 118 answers

f(x)=x3+3x27
a) Extrema point: f(x)=0
f1(x)=ddx(x3+3x27)=3x2+6x
3x2+6x=0
x(3x+6)=0
x=0,2
So, at x=2,y=8+3×47=3
Maxima (2,3)
At x=0,y=0+07=7
Minima (0,7)
b) Inflection point: f(x)=0
f2(x)=ddx(3x2+6x)
6x+6=0
x=1, so
inflection point occurs at (1,5)
c)Increasing, when f1(x)>0
3x2+6x>0
x(0,2)
Decreasing, when f1(x)<0
3x2+6x<0
x(,0)(2,)
d) Concave up: f2(x)>0
6x+6>0
x(,1)
Concave down: f2(x)>0
x(1,)

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