f(x) = 5 cos x − 5 sin x
(a) Find all points on the graph of f where the tangent line is horizontal. (Let k be any integer.)
f(x) = 5 cos x − 5 sin x take the derivative and set it to 0
f ' (x) = -5sinx - 5cosx = 0 divide through by -5
sinx + cosx = 0 subtract cos x from both sides
sinx = -cosx this occurs at 3pi/4 + k*pi where k is an integer
Thank you!!
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