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Calculus 1: Definition of the Derivative

Find the slope of the tangent line to

f(x)=1xf(x) = \frac{1}{x}

when x = 4

Use the limit definition of the derivative to find the equation of the tangent line for the graph of

y=x23x+2y = x^2 - 3x + 2 at (2, 0)

Use the limit definition of the derivative to find the equation of the normal line to the graph of

f(x)=14xf(x) = \frac{1}{\sqrt{4 - x}} at x=3x = 3

Use the limit definition of the derivative to find all points on the graph of

f(x)=4x312x2+9xf(x) = 4x^3 - 12x^2 + 9x

where the tangent lines to the graph have slope zero.