Got a Prelim on monday , please help, thanks
Q: Find the equation of the tangent to the parabola with equation
y=6+x-x(squared) at the point (1,6 ) .
If possible please explain to me how to do this question thanks .
Since you did not post this question in the Calculus subforum I assume a non-calculus approach is required ....?
Since the point (1, 6) lies on the tangent line, the equation of the tangent is where m is the gradient.
Also, the tangent (by definition) only intersects the parabola once. So the equations:
.... (1)
.... (2)
have only one solution. Solving (1) and (2) simultaneously:
.
Since there's only one solution, the discriminant is equal to zero:
.
Solve this equation for m and substitute the value into to get the final equation of the tangent.