Question 288535: find the point of inflection
f(x)= 6x-x^3
Answer by texttutoring(324)   (Show Source):
You can put this solution on YOUR website! To find inflection points, you need to find the second derivative of the function.
f(x)=6x-x^3
Use the power rule:
f'(x)=6-3x^2
Again:
f''(x)=-6x
Now set y to zero and solve for x.
0=-6x
x=0
Now put the value x=0 into the function's value to find the y-coordinate:
f(x)=6x-x^3
f(0)=6(0)-(0)^3
y=0
There is an inflection point at (0,0).
You can see this graphically by using a graphing calculator or Wolfram Alpha.
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