How To Find Points With Horizontal Tangent Line Using Derivatives In Math

how to find the points where tangent line is horizontal

find first derivative, set equal to zero, get two numbers, plug into ORIGINAL equation, form points

To find the points where the tangent line is horizontal, you need to first differentiate the given function to find its derivative. The horizontal tangent line occurs when the derivative of the function is equal to zero.

1. Find the derivative of the given function: For example, if the function is f(x) = x^3 – 3x^2 + 2x, then f'(x) = 3x^2 – 6x + 2.

2. Set the derivative equal to zero: 3x^2 – 6x + 2 = 0

3. Solve for x: You can use the quadratic formula to solve for x. x = [6 ± √(6^2 – 4(3)(2))]/(2(3)) = [6 ± √20]/6 = [3 ± √5]/3. So the two values of x where the tangent line is horizontal are [3 + √5]/3 and [3 – √5]/3.

4. Plug in the values of x into the original function to find the y-coordinate of the points where the tangent line is horizontal.

Therefore, the points where the tangent line is horizontal are [(3 + √5)/3, f((3 + √5)/3)] and [(3 – √5)/3, f((3 – √5)/3)].

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