Find the Horizontal Tangent Line y=x^2+7

Problem

y=x2+7

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. Set the derivative to zero because a horizontal tangent line occurs where the slope is equal to 0

2*x=0

3. Solve for x to find the xcoordinate where the horizontal tangent occurs.

x=0

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

y=(0)2+7

y=7

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

y=7

Final Answer

y=7

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