   Chapter 13, Problem 9RQ

Chapter
Section
Textbook Problem

# Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.9. Suppose f is twice continuously differentiable. At an inflection point of the curve y = f(x), the curvature is 0.

To determine

Whether the statement “suppose f is twice continuously differentiable, at an inflection point of the curve y=f(x) , the curvature is 0” is true or false.

Explanation

Formula used:

Consider the expression of a curvature of a plane with equation y=f(x) .

k(x)=|f(x)|[1+(f(x))2]32 (1)

At an inflection point , where f is twice continuously differentiable we must have f(x)=0

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