Let f(x) = x4-50x2/12. Use the definition of a derivative or the derivative rule
ID: 1887678 • Letter: L
Question
Let f(x) = x4-50x2/12. Use the definition of a derivative or the derivative rules to find f'(x) = Use the definition of a derivative or the derivative rules to find f''(x) = On what interval is f increasing (include the endpoints in the interval)? interval of increasing = On what interval is f decreasing (include the endpoints in the interval): interval of increasing = On what interval is f concave downward (include the endpoints in the interval)? interval of increasing = On what interval is f concave upward (include the endpoints in the interval)? interval of increasing =Explanation / Answer
F[X]=[1/12][X^4-50X^2]
A)F'[X]=[1/12][4X^3-100X] ......................ANSWER
B)F''[X]=[1/12][12X^2-100]..................ANSWER
C) F'[X]=0 AT
[1/12][4X^3-100X]=0
X[X^2-25]=0
X=0....+5 AND -5 ....
SO DEVIDING THE NUMBER LINE ALONG THESE INTERVALS
X............<-5............-5..........-5 TO 0..........0............0 TO 5 ............5 ..............>5
F'[X]=...NEGATIVE.........0........ POSITIVE.........0...........NEGATIVE...........0..........POSITIVE
HENCE WE GET
C)F[X] INCREASES IN THE INTERVALS [-5,0] AND [5,INFINITY)
D)F[X] DECREASES IN THE INTERVALS (-INFINITY , -5] AND [0,5]
E)(-INFINITY TO -5 TO 0]...AROUND X=-5
AND
[0 TO 5 TO INFINITY)....AROUND X=5
IT IS CONCAVE DOWN WARD
F)[-5 TO 0 TO 5]....AROUND X=0 , IT IS CONCAVE UP WARD
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