f\'(0)=f\'(4)=0, f\'(x)=1 if x<-1, f\'(x)>0 if 0<x<2, f\'(x)<0 if -1<x<0 or 2<x<
ID: 2887757 • Letter: F
Question
f'(0)=f'(4)=0, f'(x)=1 if x<-1,
f'(x)>0 if 0<x<2,
f'(x)<0 if -1<x<0 or 2<x<4 or x>4,
lim (x->2-) f'(x)=infinity, lim (x->2+) f'(x)=-infinity,
f''(x)>0 if -1<x<2 or 2<x<4,
f''(x)<0 if x>4.
A. Describe the portion of the curve specified by f'(0)=f'(4)=0
B. Describe the portion of the curve specified by f'(x)=1 if x<-1
C. Describe the portion of the curve specified by f'(x)>0 if 0<x<2
D. Describe the portion of the curve specified by f'(x)<0 if -1<x<0 or 2<x<4 or x>4
E. Describe the portion of the curve specified by lim(x->2-)=infinity
F. Describe the portion of the curve specified by lim(x->2+)=-infinity
G. Describe the portion of the curve specified by f''(x)>0 if -1<x<2 or 2<x<4
H. Describe the portion of the curve specified by f''(x)<0 if x>4
I. Sketch the curve from your answers to A-H
Explanation / Answer
A. Describe the portion of the curve specified by f'(0)=f'(4)=0 :
It means that for function f, this is where the function turns
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B. Describe the portion of the curve specified by f'(x)=1 if x<-1
It means the part of the curve for x <-1 is a line of slope = 1
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C. Describe the portion of the curve specified by f'(x)>0 if 0<x<2
It means f is increasing over 0 < x< 2
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D. Describe the portion of the curve specified by f'(x)<0 if -1<x<0 or 2<x<4 or x>4
It means function is decreasing over those ranges
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E. Describe the portion of the curve specified by lim(x->2-)=infinity
It means as x approaches 2 from the left, i.e values like
x = 1.99, 1.999, y starts shooting up rapidly(goes to +inf)
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F. Describe the portion of the curve specified by lim(x->2+)=-infinity
As it approaches 2 from right, i.e 2.01 , 2.001 , 2.0001 etc
y starts going downward rapidly, as in towards -inf
This indicates that there is a Vertical asymptote at x = 2
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G. Describe the portion of the curve specified by f''(x)>0 if -1<x<2 or 2<x<4
Concave up over this region, as in f would look like an upward facing U
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H. Describe the portion of the curve specified by f''(x)<0 if x>4
Concave down over this region, as in the graph would
look like a downward facing U
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