SOLUTION: Given that y=(x-3)square root x-1, find dy/dx and the value of x for which the gradient is zero.

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Question 1190932: Given that y=(x-3)square root x-1, find dy/dx and the value of x for which the gradient is zero.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
y=(x-3)*sqrt(x-1)
y'=(x-3)*1/2(sqrt(x-1)+(sqrt(x-1))
set y'=0
move one of the terms.
-sqrt(x-1)=(x-3)/2sqrt(x-1)
-2(x-1)=x-3
-2x+2=x-3
3x=5
x=(5/3) y=-1.09
graph%28300%2C300%2C-1%2C4%2C-5%2C5%2C-1.09%2C%28x-3%29%2Asqrt%28x-1%29%29
5/3 is the answer