Find the Critical Points y=x(x-2)

Problem

y=x*(x−2)

Solution

1. Expand the expression to make differentiation easier.

y=x2−2*x

2. Find the derivative of the function with respect to x using the power rule.

d(y)/d(x)=2*x−2

3. Set the derivative to zero to find the critical points, as critical points occur where the derivative is zero or undefined.

2*x−2=0

4. Solve for x by isolating the variable.

2*x=2

x=1

5. Find the y-coordinate by substituting the x value back into the original equation.

y=1*(1−2)

y=−1

Final Answer

(1,−1)

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