Find the Horizontal Tangent Line y=x^2+3

Problem

y=x2+3

Solution

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

2. Differentiate the function y=x2+3 with respect to x using the power rule.

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

3. Set the derivative equal to zero to find the xcoordinate of the point of tangency.

2*x=0

4. Solve for x

x=0

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

y=(0)2+3

y=3

6. Determine the equation of the horizontal line, which is of the form y=c

Final Answer

y=3

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