NOTATION: Pi = 3.14159... is our usual Greek number
1. [15]
Find the derivative of the following functions:
a) 3x-1/2 - (10/x7) + 3x2 - x + 1
b) (x2 - 5x) / (2 - 3x2)
c) (5x - 3)(1 - 4x2); Use the product rule here
2. [15]
a) Sketch the graph of the cube root function, f(x) = CubeRoot(x)
b) Explain why f is not differentiable at x = 0.
c) If a is different from 0, find f'(a).
3. [5]
Find the equation of the tangent line to the curve whose equation is given by
y = (6x4 - 3x2 + 1)(2 - x3) at the point (1,4).
4. [5]
Let h(x) = (2x + 1)9. Find functions f and g such that h(x) = f(g(x)), for every x.
Hint: One of the two is a power function. Also, there are many ways of doing this!
Total: 40 points