YLL討論網

1     Find the point on the graph of f(x)=4-x^2 that is closest to the point (1,0).

  2     Determine the statement "The relative maxima of the function f are f(1)=4 abd f(3)=10. so, f has at least one minimum for some x in the interval (1,3)." is true or false. If it is false, explain why or give an example that it is false.

   3     Find the rate of change of the distance between the origin and a moving point on the graph of y=sinx if dx/dt = 2 centimeters per second.

   4     The statement "function f(x)=|x-1| / (x-1) is continuous on the all real line" is ture or false?

謝謝大大

(2)
令f(x)=4     當x=1
   f(x)=10   當x=3
   f(x)=-x    當x不等於1和3的實數
則 f has at least one minimum for some x in the interval (1,3).好像不成立


(4)
這題既然問是否 continuous on the all real line 就要定義f(1)的值吧
f(x)=|x-1| / (x-1)
則
limx趨近1正f(x)= x-1 / (x-1)=1
limx趨近1負f(x)= 1-x / (x-1)=-1
limx趨近1正f(x)不等於limx趨近1負f(x)
若給f(1)有定義則 f(x)在x=1不連續