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Activity 2.7.2.
Consider the curve defined by the equation
\(x = y^5 - 5y^3 + 4y\text{,}\) whose graph is pictured in the following figure
(a)
Explain why it is not possible to express
\(y\) as an explicit function of
\(x\text{.}\)
(b)
Use implicit differentiation to find a formula for
\(dy/dx\text{.}\)
(c)
Use your result from part (b) to find an equation of the line tangent to the graph of
\(x = y^5 - 5y^3 + 4y\) at the point
\((0, 1)\text{.}\)
(d)
Use your result from part (b) to determine all of the points at which the graph of
\(x = y^5 - 5y^3 + 4y\) has a vertical tangent line.
