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Differentiability

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.

Tangent Line at a Point

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 equation of the line that passes through the point \((3,24)\) and is perpendicular to the tangent line of the curve \( y=x^2+5x\) at that point?

Given the curve \(x=t^3, y=4t^2+9,\) what is the \(y\)-intercept of the tangent line to the curve at \(t=1 ?\)

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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