Is the line y=6x−16 tangent to the curve y=x²? If yes, where? If no, prove why not.

Answer 1

y=6x-16 and y=x^2.

solve the system of equations and check for the following:

No answer: the two functions don't meet.

1 answer: The two functions are tangent

2 answers: The two functions are not tangent.

Solving we get:

6x-16 = x^2

x^2 - 6x + 16 = 0

We see that we have no answer, so the functions don't meet.