# Critical Points

The graph of f(x) = ln(x^2) has

a. neither a relative minimum nor a point of inflection at x = 0
b. a relative minimum that is not an inflection point at x = 0
c. a relative maximum that is not an inflection point at x = 0
d. an inflection point that is not a relative minimum at x = 0.

See the attached file.

# Critical points

(-x^2/2(x+1)^3/2) + (2x/(x+1)^1/2)=0

,

Critical points are any point in the domain or a function where the derivative is undefined or equals zero. The critical points are candidates for maximum and minimum values.

To find the critical points set:

=0

# Critical points

Locate all relative maxima, relative minima and saddle points for
f(x,y) = x y – x^3 – y^2 .

# Critical Points

Let f(x,y)=((x^(2)y^(2))/(x^(2)+y^(2))), classify the behavior of f near the critical point (0,0).

# Critical points

Let g(x) = 300-8x^3-x^4

-Find the local maximum and minimum values.
-Find the intervals of concavity and the inflection points.
-Use this information to carefully sketch the graph of g.

# Critical Points

“Define f(x) to be the distance from x to the nearest integer. What are the critical points of f.”

# Critical points

Attached problems no#2 and 10

Find the intervals on which f is increasing or decreasing….

# Critical points

thanks

Find the intervals on which f is increasing or decreasing. Find the local maximum and minimum values of f. Find the intervals of concavity and inflection points.

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