Find the gradient of the tangeant to the curve:
Find the coordinates of the points at the curve:
at which the tangeant is parralel to the line y - 6x = 8.
Find the coordinates of the points on the curve at which the tangeant is perpindicular to
Find the equation of the curve given and
Calculate the first derivative of f: and plug in x = 2. That means you are calculating
Rearrange the equation of the given line to: . The slope of the line is m = 6. If the tangent is parallel to this line it's slope must be 6 too. That means you are looking for those values of x that f'(x) = 6.
. Plug in this value into the equation of the function. You'll get the coordinates of the tangent point as T(1, 1)
Rearrange the equation of the line . Therefore the perpendicular direction has the slope m = 12. Thus you are looking for those values of x where f'(x) = 12:
You have to plug in these 2 values for x into the original equation of the function to get the y-coordinate of the tangent point.