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Confuzzled? 1) For both of these functios, decide whether the function is always decreasing, the function is always increasing, or the function is sometimes increasing and sometimes decreasing.
a) x^3-3x+1
b) y=1-3x-x^3
2) Find the coordinates of the point on this curve at which the gradient is zero and determine whether the point is a local maximum or local minimum, giving reasons:
y= x^2+3/square root of x
3) A circular pipe has outer diameter of 4cm and thickness t cm.
a) show that the area of cross-section, Acm^2, is given by A= pi(4t-t^2).
b) Find the rate of increase of A with respect to t when t=1/4 and when t=1/2, leaving pi in the answer.
Can someone help me with the above? It would be much appreciated.