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Christos
 3 years 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?
Christos
 3 years 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?

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0First let us factorize the original function and find its roots

Christos
 3 years ago
Best ResponseYou've already chosen the best response.0As you can see I already did that

Christos
 3 years ago
Best ResponseYou've already chosen the best response.0the roots for all 3? or just the first and second derivative?

Mertsj
 3 years ago
Best ResponseYou've already chosen the best response.01. 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]

Christos
 3 years ago
Best ResponseYou've already chosen the best response.0I am a bit confused :S hold on

Christos
 3 years ago
Best ResponseYou've already chosen the best response.0But how can I determine that info you provided above that easily

Mertsj
 3 years ago
Best ResponseYou've already chosen the best response.0You 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.

Christos
 3 years ago
Best ResponseYou've already chosen the best response.0uhm how about concave up/down  inflection points?

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

Mertsj
 3 years ago
Best ResponseYou've already chosen the best response.0Concavity 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.

Christos
 3 years ago
Best ResponseYou've already chosen the best response.0arg I think I need more practice, ill try some of these now

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Did you understand this? I had to go sorry

Christos
 3 years ago
Best ResponseYou've already chosen the best response.0factoring helps a bit maybe? or no?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0to 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
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