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Christos
Group Title
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?
 one year ago
 one year ago
Christos Group Title
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?
 one year ago
 one year ago

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Christos Group TitleBest ResponseYou've already chosen the best response.0
@Mertsj @zzr0ck3r
 one year ago

rajee_sam Group TitleBest ResponseYou've already chosen the best response.0
First let us factorize the original function and find its roots
 one year ago

rajee_sam Group TitleBest ResponseYou've already chosen the best response.0
can you do that?
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.0
As you can see I already did that
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.0
the roots for all 3? or just the first and second derivative?
 one year ago

Mertsj Group TitleBest 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]
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.0
I am a bit confused :S hold on
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.0
But how can I determine that info you provided above that easily
 one year ago

Mertsj Group TitleBest 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.
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.0
uhm how about concave up/down  inflection points?
 one year ago

Mertsj Group TitleBest 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
 one year ago

Mertsj Group TitleBest 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.
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.0
arg I think I need more practice, ill try some of these now
 one year ago

rajee_sam Group TitleBest ResponseYou've already chosen the best response.0
Did you understand this? I had to go sorry
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.0
factoring helps a bit maybe? or no?
 one year ago

Peter14 Group TitleBest 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
 one year ago
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