Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
f(x) = 3x^4  4x^3
f'(x) = 12x^3  12x^2
f''(x) = 36x^2  24x
Can you please teach me how to find increasing decreasing concave up/down infection points?
 10 months ago
 10 months ago
f(x) = 3x^4  4x^3 f'(x) = 12x^3  12x^2 f''(x) = 36x^2  24x Can you please teach me how to find increasing decreasing concave up/down infection points?
 10 months ago
 10 months ago

This Question is Closed

rajee_samBest ResponseYou've already chosen the best response.0
First let us factorize the original function and find its roots
 10 months ago

ChristosBest ResponseYou've already chosen the best response.0
As you can see I already did that
 10 months ago

ChristosBest ResponseYou've already chosen the best response.0
the roots for all 3? or just the first and second derivative?
 10 months ago

MertsjBest ResponseYou've already chosen the best response.0
1. If f '(x) > 0 for all x on (a,b), then f is increasing on [a,b] 2. If f '(x) < 0 for all x on (a,b), then f is decreasing on [a,b] 3. If f '(x) = 0 for all x on (a,b), then f is constant on [a,b]
 10 months ago

ChristosBest ResponseYou've already chosen the best response.0
I am a bit confused :S hold on
 10 months ago

ChristosBest ResponseYou've already chosen the best response.0
But how can I determine that info you provided above that easily
 10 months ago

MertsjBest ResponseYou've already chosen the best response.0
You could graph the first derivative. Or you could set it equal to 0 and solve and then test each interval to see if the derivative is positive or negative within the interval.
 10 months ago

ChristosBest ResponseYou've already chosen the best response.0
uhm how about concave up/down  inflection points?
 10 months ago

MertsjBest ResponseYou've already chosen the best response.0
That takes us to the second derivative. If the second derivative is positive, the function is concave upward. Downward if negative. Inflection point if 0
 10 months ago

MertsjBest ResponseYou've already chosen the best response.0
Concavity Theorem: If the function f is twice differentiable at x=c, then the graph of f is concave upward at (cf(c)) if f(c)0 and concave downward if f(c)0.
 10 months ago

ChristosBest ResponseYou've already chosen the best response.0
arg I think I need more practice, ill try some of these now
 10 months ago

rajee_samBest ResponseYou've already chosen the best response.0
Did you understand this? I had to go sorry
 10 months ago

ChristosBest ResponseYou've already chosen the best response.0
factoring helps a bit maybe? or no?
 10 months ago

Peter14Best ResponseYou've already chosen the best response.0
to find whether a function is increasing or decreasing, you need the first derivative. Graph the first derivative. For each xvalue: If the first derivative is positive, the function is increasing at that xvalue If the first derivative is negative, the function is decreasing at that xvalue If the first derivative is zero, the function is neither increasing nor decreasing at that xvalue. to find concavity and inflection points, you need the second derivative. Graph the second derivative. for each xvalue: If the second derivative is positive, the function is concave up at that xvalue If the second derivative is negative, the function is concave down at that xvalue If the second derivative is zero (and not constant) the function has a point of inflection at that xvalue
 10 months ago
See more questions >>>
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.