1. Find dy
dx if y =(5− 4x)
3 (2x + 7)
2. Find the equations of the tangent(s) to the curve y = x
2 that pass
through (5,9). Provide a sketch in addition to your work.
3. Consider the trapezoid formed by the 4 lines x=0, y=0, y=12 and
the tangent line to the curve y = 3x
2 − 36 at the point (4,12). Find
the area of the trapezoid.
4. Find the equation of the normal line to y = 4 1− sin2
at x = 7π
5. Write the equation of the tangent to the curve defined by y = sin2
x = cosθ
at the point where θ = π
6. Find the derivative of: f (x) = cos5x
2 + 3
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