Question

find the slope and the equation of the tangent line for y=x-cos2x at (0,-1)

Answer 1

\(y'=1+2\sin(2x)\)
So at \((0,-1)\) the slope is 1. Then the line is \(y=x+b\). Plugin \(x=0,y=-1\) we conclude that \(b=-1\). So \(y=x-1\).

Answer 2

y'=1-2(-sin(2x))=1+2sin(2x)
y'(0)=1+2sin(0)=1+2(0)=1
so the slope at (0,-1) is 1
y=mx+b equation for tangent line
y=x+b since m=1
so
(x,y)=(0,-1)
-1=0+b
b=-1
so y=x-1

Answer 3

you are a stud!