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11 Jun 2020

EXPLORING CONCEPTS

Points of Inflection

Is it possible to sketch a graph of a function that satisfies the conditions of Exercise 59 and has no points of inflection? Explain.

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Rico Jay Laxa
Rico Jay LaxaLv10
12 Jul 2020

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Sketch a graph of a differentiable function f that satisfies the following conditions and has as its only critical number.

EXPLORING CONCEPTS

Sketching a Graph

In Exercises 51 and 52, sketch the graph of an arbitrary function f satisfying the given conditions. State whether the function has any extrema or saddle points. (There are many correct answers.)

and for all .

Points of Inflection

(a) Let , be a quadratic polynomial. How many points of inflection does the graph of f have?

(b) Let , be a cubic polynomial. How many points of inflection does the graph of f have?

(c) Suppose the function satisfies the equation

where k and L are positive constants. Show that the graph of f has a point of inflection at the point where . (This equation is called the logistic differential equation.)

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