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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem

Using the Second-Derivative Test In Exercises 39–50, find all relative extrema and points of inflection. Then use a graphing utility to graph the function.

f ( x ) = 2 x + 3 x

To determine

To calculate: The relative extrema and point of inflection of the function g(x)=2x+3x by use a graphing utility to graph the function.

Explanation

Given information:

The provided function is g(x)=2x+3x.

Formula used:

Use second derivative test to find relative maxima and minimum of a function,

1. If f(c)>0, then f(c) is a relative minimum.

2. If f(c)<0, then f(c) is a relative maximum.

3. If f(c)=0, test fails use first derivative test whether f(c) is a relative minimum, is a relative maximum or neither.

Calculation:

Consider the function,

g(x)=2x+3x

Now, find the first derivative,

g(x)=2x+3xg(x)=x1232x32=1x1232x32=1x1232x32

So, critical points is x=32

Now, find second derivative and per second derivative test,

g(x)=x1232x32g(x)=12x32+94x52=12x32+94x52=2x+94x52

So, the results are shown in the table,

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