Find the Horizontal Tangent Line y=x^2+2x

Problem

y=x2+2*x

Solution

1. Find the derivative of the function to determine the slope of the tangent line at any point x

d(y)/d(x)=2*x+2

2. Set the derivative to zero because a horizontal tangent line occurs where the slope is zero.

2*x+2=0

3. Solve for x to find the xcoordinate of the point where the tangent is horizontal.

2*x=−2

x=−1

4. Substitute the x-value back into the original function to find the corresponding ycoordinate.

y=(−1)2+2*(−1)

y=1−2

y=−1

5. Identify the equation of the horizontal line, which is in the form y=c

y=−1

Final Answer

y=−1

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