Show that the graph f(x)=(x^3)+(2x^2)+6x does not have a tangent line with a slope of 4.
Im not really sure where to start with this one...find f'(x) first or what?
Find and show it can never equal .
Show has no real solutions.
Spoiler:
Use the quadratic formula on , so , , and .
So there are no real roots, and therefore the slope of the tangent line never equals . (You actually could have stopped as soon as you saw that the discriminant in the quadratic formula was negative, but I figured I'd finish it out to the end.)