anonymous
  • anonymous
f(x) = x^3 + 8x - 19 Show that the equation f(x)=0 has only one real root.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
I can only recommend the Newton-Method or the Method of Bisection for this problem.
ZeHanz
  • ZeHanz
It is a polynomial of the 3rd degree. Look at the end-behaviour of the function: The limit of f(x) if x => infinity is also infinity. The limit of f(x) if x => -infinity is also -infinity. f is continuous for every x, so it must be 0 at least one time. Now look at the derivative: f'(x)=3x²+8. What do you know about the possible values of f' ?
anonymous
  • anonymous
Yeah, you know it has to have one because there is a change in sign basically. And are you saying that f'(x) will never be zero so there's no turning point?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
Or that it's always positive.
ZeHanz
  • ZeHanz
That is just what I wanted to say ;) So f is always increasing...
anonymous
  • anonymous
Good man!
ZeHanz
  • ZeHanz
YW!

Looking for something else?

Not the answer you are looking for? Search for more explanations.