What means zero derivative for the function y=x^2-6x+3?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

If the derivative of a function is 0, it indicates an extreme point.

y = x^2 - 6x + 3

y' = 2x - 6

If y' = 0

=> 2x - 6 = 0

=> x = 3

f(3) = 3^2 - 6*3 +3

=> 9 - 18 + 3

=> - 6

At x = 3, we have a minimum value equal to -6.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Zero derivative of a function means that the function has a local extreme point, minimum or maximum, for a root of 1st derivative of the function.

The root of derivative represents the critical point of the function.

Usually, we'll determine zero derivative when we want to find out the extreme points of the function.

For instance, we want to determine the zero derivative of the function:

y = x^2 - 6x + 3

dy/dx = 2x - 6

2x - 6 = 0

2x = 6

x = 3

So, x = 3 is the zero derivative and it represents the critical point and f(3)=9 - 18 + 3 = -6 => f(3) = -6 represents the minimum point of the function.

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