Mathematics 1 Deneme Sınavı Sorusu #1357111

At which (x,y) point is the value of the function y=f(x)=x2-6x+5 is minimum?


(0,5)

(3,0)

(6,1)

(2,-3)

(3,-4)


Yanıt Açıklaması:

The first derivative must be equal to zero and the second derivative must be positive for a minimum value of a function. Thus:

f(x)=x2-6x+5

f'(x)=2x-6=0 so 2x=6, x=3 and when x=3 y=f(x)=9-18+5=-4

The second derivative is:

f''(x)=2>0

Thus for given function, point (3,-4) is the minimum.

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