Answer to Question #4702 in Calculus for dana

Question

find the slope of the tangent line to y=2/3x^2-x/6 at (-1,5/6)

Answer 1

The slope of the tangent line can be found according to this formula: y' = tan(α). So we have to differentiate the equation y=2/3x^2-x/6 to get y'.

So we have y' = (4/3x - 1/6) and if we replace the variable by the number of (-1,5/6) we will get tan(α) = y' = -1/2.
Finaly to get α we make atan(-1/2) = α. So α = atan(-1/2) or 26.565 degrees.