Those friendly functions that don't contain breaks, bends or cusps are "differentiable". Take their derivative, or just infer some facts about them from the Mean Value Theorem.

Which of the following is the tangent line to the curve \(f(x)=2x^3-8x^2\) at the point \((1,-6)?\)

Find the equation of the tangent line to the curve \(x^2y-x=4y^3-108\) for \(x=0.\)

What is the \(y\)-intercept of the tangent line to the curve \(y=e^{x-4}\) at the point \((5,e)?\)

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