Differentiation and applications

Analysing the behaviour of functions using the second derivative

(* Ignore this section* - wk 5, 5c Q 10-13) )

Please answer the questions on the attachment below. ( ON PAPER/WRITTEN ) ( Please keep solving and explanation seperate)

10 Show that the maximum value of the gradient to the curve f(x) = x3 + 3x2 + 2 is 3. l 1 Find the maximum value of the gradient to the curve y = 10 + 3x2 2x3. 12 Sketch the graph of the function y = x4 x2 12, showing all intercepts with the axes, the stationary points and any points of inflection. (Verify with a graphics calculator.) 13 The downward displacement of a meteor 1' seconds after hitting the surface of the ocean is given by: :2 '3 d:40t+Z,whereOSrSZOanddisinmetres. Find the depth of the meteor after 10 seconds. Find the velocity. v, at any time I. Find the maximum velocity of the meteor. If the depth of the ocean where the meteor strikes is 600 metres and the meteor disintegrates 20 seconds after hitting the ocean, does the meteor reach the ocean oor? D.\" O'D