A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
Explain why f(x)=4x^7+7x^3+9x357 does not have a tangent line with a slope of 1.
anonymous
 5 years ago
Explain why f(x)=4x^7+7x^3+9x357 does not have a tangent line with a slope of 1.

This Question is Closed

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we can take the derivative of it and try to make it equal 1

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0f(x)= 4x^7+7x^3+9x357 f'(x)= 28x^6+21x^2+9 = 1 28x^6 +21x^2 +8 = 0 has the same effect

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we can use synthetic division and trial and error to try to come to the roots...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.01, 2, 4, 7, 14, 28  these numbers will give us a "pool" of options 1, 2, 4, 8 that we can use to determine its roots

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0then its just a matter of digging in and getting dirty :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i was told that the answer has to do with the degree of the polynomial (the derivative polynomial the 28x^6+21x^2+9)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0im sure it does, but without any prior knowledge about any shortcuts, this is how I would go about convincing someone that there is no slope of 1

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0there are therums with names that I dont remember that tell you if the signs are all positive, then there is no positive root....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lets try x = 1 on this...  1  28 0 0 0 21 0 9 0 28 ........ 28......49  28 28 ......... 49......58 since all our answers are positive, then (x1) and higher are not going to be answers

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[x^{2n} \geq 0\ \forall{ x \in \mathbb{R}; n \in \mathbb{Z}}.\] Therefore it is > 0 ...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry, the LaTeX engine on this thing is pellet so those conditions may be a little odd looking

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0since 1 is not a root, it leads me to believe that there is no tangent to the curve that has a slope of 1....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0x^{even} >= 0 for all x

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0that "A" means all x elements of R right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So it + 9 > 1 for all x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well the polynomial does not even hits the xaxis so there can't be any roots for the polynomial i guess; they're all imaginary roots

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0if the graph of the derivative doesnt hit the x axis, then right, there are no real root...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Tangent with gradient 1 iff f'(x) = 1 iff 28x^6+21x^2+9 = 1 iff 28x^6+21x^2 + 8 = 0 , from above. And I have just told you that the first part is always >= 0 .

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes, listen to amistre

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok, well thanks to both of you
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.