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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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