Find the Horizontal Tangent Line y=2x^2+4x-7

Problem

y=2*x2+4*x−7

Solution

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

2. Differentiate the function with respect to x using the power rule.

d(y)/d(x)=4*x+4

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

4*x+4=0

4. Solve for x by subtracting 4 from both sides and dividing by 4

4*x=−4

x=−1

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

y=2*(−1)2+4*(−1)−7

y=2−4−7

y=−9

6. Write the equation of the horizontal line, which is in the form y=k where k is the ycoordinate found.

Final Answer

y=−9

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