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?
Hi
Yes , you differentiate first to find the gradient of the tangent line .
$\displaystyle f'(x)=3x^2+4x+6 $
Now check its discriminant
$\displaystyle b^2-4ac=4^2-4(3)(6)=-56<0$
Since its smaller than 0 , hence it has no real roots , which means no value of x would give you 4 , which is the gradient of the tangent line .