Find the equation of the line that is tangent to the curve
y = 3xcosx
at point (pi, -3pi)
The equation of this tangent line can be written in the form y=mx+b
-Would appreciate any help on solving this one!
I solved it. The solution is y=-3x
(as b=0)
Thanks all for the help.
y = 3xcosx
and the slope at any point on this cure is given by the derivative of this function.....so we have....
y ' = 3cosx - 3xsinx = 3[cosx -xsinx]
So, the slope at (pi, -3pi) =
y '(pi) = 3 [ cos (pi) - (pi) sin (pi)] = 3 [-1 - pi*0] = 3 [-1] = -3
And the equation of the tangent line at this point =
y - (-3pi) = -3(x - pi)
y + 3pi = -3x + 3pi
y = -3x