{ f(x) = x^n } , where n is a positive integer greater or equal to 2. The graph of f(x) will...

Question:

{eq}f(x) = x^n {/eq} , where n is a positive integer greater or equal to 2. The graph of f(x) will have an inflection point when n is

A. Even

B. Odd

C. Divisible by 3

D. For all values

E. For no values

Inflection Point:

{eq}\\ {/eq}

An inflection point is such a point on the curve where change in the direction of curvature occurs. For a function, say {eq}f(x) {/eq}, the inflection point can be found by setting {eq}f''(x)=0 {/eq}.

It may be a stationary point on the curve but cannot be local maxima or minima. When {eq}f''(x)<0 {/eq}, the function is concave downwards whereas when {eq}f''(x)>0 {/eq}, the curve is concave upwards.

Answer and Explanation:

{eq}\\ {/eq}

B. ODD

When {eq}n {/eq} will be odd then {eq}f''(x) {/eq} will result in odd power of {eq}x {/eq} which will change its sign crossing {eq}x=0 {/eq} which will become its inflection point.


Learn more about this topic:

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Concavity and Inflection Points on Graphs

from Math 104: Calculus

Chapter 9 / Lesson 5
6.8K

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