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Calculus

Differentiability

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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