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Show that the equation $y=e^x/x^3$ has a root between $1.2$ and $1.3$

Hey, having trouble with this one. Would appreciate a hand, not sure how to go about the exponent and such.

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madbro13
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    can you check whether you have typed the question correctly? – Siong Thye Goh Aug 10 '18 at 00:48
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    What do you mean? As $x$ goes from $1.2$ to $1.3$, $e^x/x^3$ goes from approximately $1.92$ to approximately $1.67$. Are you supposed to take some $y$ in that interval? – Robert Israel Aug 10 '18 at 00:50
  • I typed the question correctly yes, @RobertIsrael I got those as well but im not sure if its right, as I read that to prove it has a root there needs to be a negative value? Im really new to this so I don't really have a clue, heres part B if it helps make sense. – madbro13 Aug 10 '18 at 00:53
  • Use the Newton-Raphson method to find the value of the root correct to seven significant figures. – madbro13 Aug 10 '18 at 00:53
  • There must be a mistake in the question, then. – Robert Israel Aug 10 '18 at 01:38

1 Answers1

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For $x>0$, $\frac{\exp(x)}{x^3} >0$, it is not a true statement.

For $x<0$, $\frac{exp(x)}{x^3} < 0$, it doesn't have a root.

The function is not defined at $x=0$.

It doesn't have a root.

Here is how it looks like:

enter image description here

Desmos link here.

Siong Thye Goh
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