Reference no: EM131006842
1. Let f{x) = ¼ x3 + 4.
a. Sketch a graph of y = f(x) and explain why f is an invertible function.
b. Let g be the inverse of f and determine a formula for g.
c. Compute f'(x), g'(x), f'(2), and f'(6). What is the special relationship between f'(2) and g'(6)? Why?
2. Consider the curve defined by the equation x = y5 - 5y3 + 4y, whose graph is pictured in Figure.
a. Explain why it is not possible to express y as an explicit function of x.
b. Use implicit differentiation to find a formula for dy/dx.
c. Use your result from part (b) to find an equation of the line tangent to the graph of x = y5 - 5y3 + 4y at the point (0,1).
d. Use your result from part (b) to determine all of the points at which the graph of x = y5 - 5y3 + 4y has a vertical tangent line.
Figure: The curve x = y5 - 5y3 + 4y.
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Find all of points at which graph has vertical tangent line
: Use your result from part (b) to determine all of the points at which the graph of x = y5 - 5y3 + 4y has a vertical tangent line. Use implicit differentiation to find a formula for dy/dx.
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