Your function
has slope 6.
Your function
has derivative:
which has slope 6 at x=3. Thus y = 9. The tangent line must be y=6x-9.
Hello all! I just found this forum and registered. I would like some help with the following problem:
What is the function of the tangent to the parable , parallell with the line ? I can see where the tangent is graphically and go from there, but how can you solve it solely by equating?
(feel free not to copy my terminology; I'm not good at English and may use some odd names)
Here is a different approach:
The tangent line has the equation:
Now calculate the coordinates of the intersection between the parabola and the straight line:
Use the formula to solve this quadratic equation:
You get only one intersection point (=tangent point) if the radicand equals zero:
. Consequently the tangentpoint is T(3, 9)
Therefore the equation of the tangent line becomes: