Question

Determine the point(s) (if any) at which the graph of the function has a horizontal tangent line. y = √3x + 2 cos x, 0≤ x < 2π

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ddx[3x]+ddx[2cos(x)]=3ddx[x]+2ddx[cos(x)]=32sinx\frac{d}{dx}[\sqrt{3}x]+\frac{d}{dx}[2cos(x)]=\sqrt{3}\frac{d}{dx}[x]+2\frac{d}{dx}[cos(x)]=\sqrt{3}-2\sin{x}

A horizontal tangent line has a slope of zero, therefore we need to find the points where the graph of the function has a slope of zero. The slope of a function is the function of its instantaneous rate of change or its derivative. So first we need to find the derivative.

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