Differential Calculus_Max and Min

Those values in which f’(x)=Undefined

• Critical point

• Inflection point

• Stationary point

• Extrem values

• Singular points

Those points known as maximun and minimun.

• Critical point

• Inflection point

• Stationary point

• Extrem values

• Singular points

Is a point with f’(x)=0, this can be extrem values and inflection points.

• Critical point

• inflection point

• Stationary point

• Extrem values

• Singular points

Is a point where f’(x)=0 or undefined, this can be, stationary points, singular points, inflection points

• critical point

• inflection point

• stationary point

• extrem values

• singular points

Use the criteria of the first derivate to locate all the extrem points in f(x).

• local maximum at x=-1, and minimum in x=3

• local minimum at x=3, and maximum at x=-1

• local minimum at x=3, inflection point in x=0 and minimum in x=-1

Look to this graph, how many and which kind of critical point do you observe.

• 3 critical points: maximum, minimum and inflection points

• 3 critical points: maximum, minimum and singular point

• 2 critical points: maximum and minimum

Where increase and where decrease the function f(x)=2x³-3x²-12x+7

• increase in the interval (-inf, 1] and decrease [1,3]

• increase from (-inf,-1], [1,inf) and decrease [-1,2]

• increase from (-inf,-1] and decrease [-1,2], [1,inf)

Which do you think is the easiest form to known if a extrem value is a local or global maximum or minimum ?

• Just making f'(x)=0

• By calculating f'(a)

• Making the substitution of the critical points on f(x) and comparing

• Making the substitution of the critical points on f''(x) and comparing

Select the local maximum, local(relative)minimum, global maximum, global minimum in the picture

• Local Maximum:G, Local Minimum:F, Global maximum:B, Global Minimum:C

• Local Maximum:G, Local Minimum:N/A, Global maximum:B, Global Minimum:F

• Local Maximum:G, Local Minimum:C, Global maximum:B, Global Minimum:N/A

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