Determine the coordinates of the indicated point by plugging the value of x into the function. For example, to find the tangent line where x = 2 of the function F(x) = -x^2 + 3x, plug x into the function to find F(2) = 2. Thus the coordinate would be (2, 2).
Find the derivative of the function. Think of the derivative of a function as a formula that gives the slope of the function for any value of x. For example, the derivative F'(x) = -2x + 3.
Calculate the slope of the tangent line by plugging the value of x into the function of the derivative. For example, slope = F'(2) = -2 * 2 + 3 = -1.
Find the y-intercept of the tangent line by subtracting the slope times the x-coordinate from the y-coordinate: y-intercept = y1 - slope * x1. The coordinate found in Step 1 must satisfy the tangent line equation. Therefore plugging in the coordinate values into the slope-intercept equation for a line, you can solve for the y-intercept. For example, y-intercept = 2 - (-1 * 2) = 4.
Write the equation of the tangent line in the form y = slope * x + y-intercept. In the example given, y = -x + 4.