posted by Daniel on .
-find the equation of the tangent line to the curve y=5xcosx at the point (pi,-5pi)
-the equation of this tangent line can be written in the form y=mx+b where
-what is the answer to m and b?
and the equation of the tangent passing through the point (x0,y0)=(π, -5π) is:
Substitute values and simplify to get the equation of the line.
and b= y-pi=pi(x+5pi)
m=pie but what does b= though
We have established:
=5(-1 - π*0)
The equation of a line of slope m passing through (x0,y0) is:
Simplify to get the required equation.
b=0 by coincidence.
Check my work.
you did not follow MathMate's suggestion
f'(x) = 5(cosx - xsinx)
f'(π) = 5(cosπ - πsinπ)
= 5(-1 - π(0)) = -5 , so m = -5
y = -5x + b , but (π,-5π) lies on it, so
-5π = -5(π) + b
b = 0
equation : y = -5x
or using MathMate's suggestion:
y + 5π = -5(x-π)
y + 4π = -5x + 5π
y = 5x
ok how about this one:
this is what i did:
is that right what am i doing wrong and what would be the answer