By using Rolle's theorem it is impossible for the function f(x)=(x^5) + x - 12 to have two real roots. This is because if f(x) has two real roots then by Rolle's theorem, f '(x) must be _________ at certain value of x between these two roots, but f '(x)  is always positive.

Question
Asked Apr 26, 2019
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By using Rolle's theorem it is impossible for the function f(x)=(x^5) + x - 12 to have two real roots. 

This is because if f(x) has two real roots then by Rolle's theorem, f '(x) must be _________ at certain value of x between these two roots, but f '(x)  is always positive.  

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Expert Answer

Step 1

The complete sentence should be as shown below:

This is because if f(x) has two real roots then by Rolle's theorem, f '(x) must be zero at certain value of x between these two roots, but f '(x)  is always positive.  

Step 2

Let's prove this by contradiction.

Let's assume f(x) = x5 + x - 12 has two real roots, say a and b and without loss of generality, let's further assume a < b

Then f(a) = f(b) = 0

As per Rolle'...

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Math

Calculus