Find the Horizontal Tangent Line y=3x^2+4x

Problem

y=3*x2+4*x

Solution

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

2. Find the derivative of the function y=3*x2+4*x with respect to x using the power rule.

d(y)/d(x)=6*x+4

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

6*x+4=0

4. Solve for x by subtracting 4 from both sides and then dividing by 6.

6*x=−4

x=−2/3

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

y=3*(−2/3)2+4*(−2/3)

6. Simplify the expression to determine the constant yvalue of the horizontal line.

y=3*(4/9)−8/3

y=4/3−8/3

y=−4/3

Final Answer

y=−4/3

Want more problems? Check here!