anonymous
  • anonymous
Show that f(x) = x^3 and g(x) = 200x^3 grow at the same rate.
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.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
SolomonZelman
  • SolomonZelman
do they really?
anonymous
  • anonymous
I'd honestly say g(x) grows faster but I'm not quite sure on how to justify it.
SolomonZelman
  • SolomonZelman
You are not just shifting the functions to the side or up/down. You are multiplying times a scale factor, and that means that slope will differ.

Looking for something else?

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

More answers

SolomonZelman
  • SolomonZelman
Well, your g(x)=f(x)•200
SolomonZelman
  • SolomonZelman
What kind of prove.reasoning do you want? maybe we can show that for every positive k, the function g(x) will have a bigger rate of change at every point?
SolomonZelman
  • SolomonZelman
(or a bigger magnitude of the slope \(\forall k\in \mathbb{Z} \))
SolomonZelman
  • SolomonZelman
\(\large\color{#000000 }{ \displaystyle f'(x)=3x^2 }\) \(\large\color{#000000 }{ \displaystyle g'(x)=600x^2 }\) \(\large\color{#000000 }{ \displaystyle 3x^2\le 600x^2 \quad \forall x\ne0}\)
anonymous
  • anonymous
So you just took the derivative? And the one with the larger one has a faster rate of growth?
anonymous
  • anonymous
It asks me to show so I'm guessing what you did is what they're looking for.
SolomonZelman
  • SolomonZelman
Yes, because the derivative itself is slope, by defnition.
anonymous
  • anonymous
I don't really believe there is anything more to be said about this. We can't explain common sense
anonymous
  • anonymous
Larger slope is equal to a faster rate of growth
SolomonZelman
  • SolomonZelman
Yes, fabulous!
anonymous
  • anonymous
Thanks for your help
SolomonZelman
  • SolomonZelman
Anytime

Looking for something else?

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