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 3 years ago
guys help me find the concavity of f(x)= x^44x^3+4x^2. i kow the procedure but have problems with calculations. so helpp
 3 years ago
guys help me find the concavity of f(x)= x^44x^3+4x^2. i kow the procedure but have problems with calculations. so helpp

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across
 3 years ago
Best ResponseYou've already chosen the best response.0Differentiate this function twice.

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.2f(x)=x^44x^3+4x^2 f'(x)=4x^312x^2+8x f''(x)=12x^224x+8 let's find the inflection points where the curve changes concavity f''(x)=0 x=1+ 1/root 3 and 11/root 3 so x =0.42 and 1.577 here the curve changes concavity if f''(x)>=0 then f(x) is concave up if f''(x)<=0 then f(x) is concave down for the interval (infinity, 0.42] and [1.577, infinity) f(x)''>=0 for the interval[0.42,1.577] f''(x)<=0 so f(x) has concavity up in the interval(infinity, 0.42] and [1.577, infinity) and concavity down in [0.42, 1.577]

suju101
 3 years ago
Best ResponseYou've already chosen the best response.0is it correct to get intervals in decimal??

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.2yeah, you can also write in radical like 1+1/root 3

suju101
 3 years ago
Best ResponseYou've already chosen the best response.0plz help me with this f(x)=x^3/(3x^2+1). for the same thing. i messed up while solving.

PROSS
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1325942133129:dw First step find the first derivative

PROSS
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1325942270219:dw simplify more

PROSS
 3 years ago
Best ResponseYou've already chosen the best response.0Now take the derivative again....

PROSS
 3 years ago
Best ResponseYou've already chosen the best response.0set = to 0 and solve to determine possible points of inflection...then choose values to the left and right of these zeros to determine if x>0 concave up or if x<0 concave down....
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