Question

Find all points (x,y) on the graph of f(x)=2x^2-3x with tangent lines parallel to the line y=9x+4

Answer 1

we have to compute the first derivative of your function, first

Answer 2

do you know how to compute such first derivative?

Answer 3

yes i do

Answer 4

it would be 4x-3

Answer 5

ok! now using the geometrical meaning of the first derivative, we have to solve this equation:
\(4x-3=9\)
being \(9\) the slope of the line

Answer 6

please solve that equation with respect to \(x\)
what do you get?

Answer 7

x=3

Answer 8

correct!

Answer 9

we got only one x-coordinate, so the y-coordinate is:
\(y=2\cdot 3^2-3\cdot 3=...\)

Answer 10

y=9

Answer 11

correct! So the requested point is \((3,9)\)

Answer 12

It says all points is (3,9) the only one?

Answer 13

yes! It is the only point, since the first derivative is a polynomial of degree 1

Answer 14

Ok thank you very much

Answer 15

:)