Find the Horizontal Tangent Line y=x^2+1

Problem

y=x2+1

Solution

1. Identify the condition for a horizontal tangent line, which occurs when the slope of the function is zero.

2. Find the derivative of the function y=x2+1 with respect to x to determine the slope formula.

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

3. Set the derivative equal to zero to find the xcoordinate where the tangent line is horizontal.

2*x=0

4. Solve for x by dividing both sides by 2

x=0

5. Substitute the xvalue back into the original equation to find the corresponding ycoordinate.

y=(0)2+1

y=1

6. Write the equation of the horizontal line passing through this point.

Final Answer

y=1

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