A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
Find the equation of the line tangent to the graph of x^3  4x^2 + 5x with the least slope. What can I do on this one?
anonymous
 4 years ago
Find the equation of the line tangent to the graph of x^3  4x^2 + 5x with the least slope. What can I do on this one?

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0have you studied calculus?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes. i think i should take the first derivative of this function and minimize it on the interval \[\left( \infty ,\infty \right)\] i found that at x=4/3, it's slope will be least. i don't know what to do next.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0well the equation of the tangent at x = 4/3 is value of the the function at x=4/3 just plug in this value of into f(x)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0differentiate 3x^2  8x + 5 = 0 for critical points (3x 5)(x  1) = 0 x = 5/3 or x = 1 there are two turning points second derivative = 6x8 so x = 5/3 gives minimum and x=1 gives maximum

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0there are two tangents with slope zero at x=1 and at x=5/3

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ah. but when you get the critical points of the first derivative, you are minimizing the value of the original function and not its slope. am i making sense?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes the critical points give you local minimum and local maximum of the original function or it could be a point of inflection. The tangents to the graph at these max and min points will have 0 slope. The question is a bit confusing it asks for the tangent (singular) with least slope but there are two of these. i'll try and draw it

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1327319828466:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0excuse the bad drawing!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i think we can get a single tangent line by just minimizing the second first derivative. love the drawing.
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.