Question
Asked Nov 27, 2019
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Consider the following function: 

F(x) = x^5 + 2x^4

Identify the following:

d. Intervals where the function is increasing/decreasing

e. Local extrema, give the location and value for any local maxima/minima

f. Concvity of the function and Points of Inflection (if they exist)

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Expert Answer

Step 1

Part (d):

Increasing and decreasing:

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Given: F(x)x5+2x4 Step 1: Find critical points: F-0. Differentiate the function F with respect to x X5+2x4 F'(x) dx F'(x)5x4 +(2x4)x F'(x)-5x4+83 0= 5x4 +8x3 0=x3(5x+8 x30 or 5x+8=0 The critical point :x=0,- 5

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Step 2

Step 2: Test points to find interval increasing or decreasing.

If F’(x) >0, the function is increasing.

If F’(x) <0, the function is increasing.

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0,0<x<) Interval from critical points <x<- 5 Choose test points in intervals (0<x< 8 -o<x<- 5 8 <x<0 5 Test points sign x =1 Positive x=-1 x=-2 Positive Negative decreasing Increasing Increasing Behaviour

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Step 3

Part (e):

The sign changes + to – in F’(c...

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8 At the point x=- 5 is positive and the interval<x<0is The interval <- 5 8 negative, and then x=-' is Local Maximum in F(x) Substitute = 5 4 8192 3125 +2 5 F 5 8 8192 Local Maximum: 5 3125

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Tagged in

Math

Calculus

Functions