Approximate a critical number of y = x^3 + e^−x using Newton’s method

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Approximate a critical number of y = x^3 + e^−x using Newton’s method

Mathematics
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Critical numbers are where the derivative is 0 or doesn't exist. Did you find the derivative?
Ohh okay got it! I was a little confused on what it was xD
ok

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Wait so the derivative is \[3x^2 - e^x\] right?
\[3x^2-e ^{-x}\]
hmm okay! thanks :)
I think I'm doing this completely wrong lol... I misunderstood the question!
Approximate a critical number of y = x^3 + e^−x using Newton’s method
That's the question
Not really sure how many roots the derivative has, but I guess start with xn = 0 |dw:1435192530939:dw|
|dw:1435192671369:dw| Then keep going until the numbers don't change much
Ohh So the same process is just repeated over an over?
and*
|dw:1435192838109:dw| wrong equation. Thanks to @jim_thompson5910 for pointing it out
Ahh I see
What is this equation called?
Newton's method
Ohh so every time I have to use newton's method I just apply this?
yes where the first term \(\Large x_0\) is the initial guess. You can randomly pick a number (say 0) or look at the graph and make an educated guess where the root is
x1 is generated from x0 x2 is generated from x1 etc etc the further you go, the more accurate the approximation
Oh I understand! Thanks so much!
no problem

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