For each problem, find the x-coordinates of all points of inflection, find all discontinuities, and find the open intervals where the function is concave up and concave down.   y = 1 / ( x-3)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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For each problem, find the x-coordinates of all points of inflection, find all discontinuities, and find the
open intervals where the function is concave up and concave down.

 

y = 1 / ( x-3) 

Expert Solution
Step 1

Consider the given function,

y=1x-3

It can be observed that,

x-3=0x=3

So the function is discontinuous at x=3.

Now, find the second derivative,

dydx=ddx1x-3=-1x-32d2ydx2=ddx-1x-32=2x-33

Now, it can be observed that,

x-3=0x=3

when x=3 the denominator will be zero then it will be undefined.

So, x=3 is an inflection point.

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