1.) Find all values of x for which the line that is tangent to y = 3x - tanx is parallel to the line y - x = 2
ALWAYS remember that when you differentiate you are finding the gradient to the tangent of a curve
$$\\y=3x-tanx\\
y'=3-sec^2x\\\\
y-x=2\\
y=x+2\\
y'=1\\\\
1=3-sec^2x\\
-2=-sec^2x\\
2=sec^2x\\
\frac{1}{2}=cos^2x\\
cos x = \pm\frac{1}{\sqrt2}\\
x= n\pi\pm \frac{\pi}{4}\qquad n\in Z$$
1.) Find all values of x for which the line that is tangent to y = 3x - tanx is parallel to the line y - x = 2 - See more at: http://web2.0calc.com/questions/stuck-on-calculus#sthash.cD8MZGpc.dpuf