Question
Asked Oct 23, 2019
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Where is the function concave upward and concave downward?

f(x)=5x^7-28x^5

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Expert Answer

Step 1

The given function is,

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f (x) 5x-28x

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Step 2

Find the derivative of the function f(x).

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f'(x)=35x° -140x f (x) 210x-560x Obtain the inflection points Solve f"(x)0. 210x3560x = 0 10x2 (21-56)= 0 10x0 or 21x2 -56 0 56 х3D0 or x? 21 212 х- 0 or x —+. 3

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Step 3

The intervals of t...

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212 3 3 Check the sign of the function Interval Functional value Sign 22 -o, 3 f(-2)- 210(-2)-s60(-2) =-6720 4480 < 0 2/2 f(-1)210(-)-560(-1) =-210 +560 0 2/2 0, 3 f()-210(1)-560(1 210-560 <0 2/2 f(2) 210(2)-560(2) 3 = 6720-4480 >0

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