Calc 1 chapter 2 homework

Question

Find equations of both lines through the point (2, −3) that are tangent to the parabola y = x2 + x.

Y= ( ) smaller slope

Y= ( ) larger slope

Answer 1

Let x,y be the point of tangency

The slope of the tangent is 2x+1

but it is also given by (x² + x +3)/x-2

Therefore, x² + x + 3 = (2x+1)(x-2) = 2x² - 3x -2

and

x²-4x-5=0 so that x=-1 and x=5 give you the abscissa of the point on the parabola.

You should be able to compute the slope for each x value.