Question

Find the equation of the tangent line to the curve at the given point y=cosx-sinx [pi,-1]

Answer 1

The slope is the derivative, so you will need to differentiate the function.

Your function is: \(\large\color{black}{ \displaystyle f(x)=\cos x-\sin x }\)
The derivative is: \(\large\color{black}{ \displaystyle f'(x)=? }\)

Answer 2

then, after you find the derivative, plug in \(\pi\) into the derivative, to find the slope at \(x=\pi\).

Answer 3

The tangent line will be:

\(\large\color{black}{ \displaystyle y-y_1=m(x-x_1) }\)

\(\large\color{black}{ \displaystyle y-(-1)=f'(\pi)~(x-\pi) }\)

\(\large\color{black}{ \displaystyle y=-1+f'(\pi)~(x-\pi) }\)

Answer 4

recalling the fact that \(f(\pi)=-1\), all you are doing is writing a 1 degree tailor polynomial for your initial function at \(x=\pi\)