Question

Find the x-coordinate where the graph of the function f(x) = e(–cosx) has a slope of 0.

Answer 1

The slope of the tangent line to
`f(x)` through the point
`(x,f(x))` is given by the derivative:


`f(x)=e^(-\cos x)\implies f'(x)=e^(-\cos x)\sin x`

The value of the derivative is zero when
`\sin x=0`, which happens for infinitely many points
`x=n\pi` where
`n` is any integer.