I am trying to do this question with out derivatives for about 45 min and i still don't know what to do. any help would be appreaciated. Thank you.
find the coordinates of the point on the point on the curve f(x)=3x^2 -4x where the tangent is parallel to the line y=8x.
I know that the slope of the tangent is 8, but i am not sure how to proceed.
Well, first, the "slope" is a number and so is not "parallel" to anything, but I understand what you mean- the tangent line is parallel to y= 8x and so the slope is 8. The limit of the difference quotient must be 8. The difference quotient is . Taking the limit as h goes to 0 gives you a function of x. Set it equal to 8 and solve for x.
By the way, another way to find a tangent is to use Fermat's method of "ad-equation" which he developed literally "precalculus". Obviously, will be equal to where they intersect- but there will be a double root for (x, y) where they are tangent. The quadratic equation will have a double root where its discriminant, . Knowing that the slope is a= 8 reduces that to a simple equation for b and then you can find the correct x and y values.