section12: dy/dx graphomg! dy/dx! differentiation! OH NO i shall just give up T.T
nah joking. this section is nowhere as difficult as you'd think. it's just transformation you know, possibly the simplest mathematics topic ever taught!
the dy/dx graph is just a graph of the
gradient of the orignal curve. i.e. a
graph of all the dy/dx values.one simple way of deriving this graph is of cause using the all powerful GC! but still, nothing's greater than the human mind, so here's what you got to learn to win that little (but heavy) gadget:
ah, the same y=f(x) graph
recall that in differentiation, when
x=turning point, dy/dx=x-intercept!
using differentiation (or eye power!),
deduce positive gradient and negative gradient.
hence the for points where x<3,>3, the gradient is positive.
thus this is the dy/dx graph that you will obtain:
easy peasy piece of cake xD
e.g. a random y=f(x) graph. observe how the gradients (dy/dx values) are obtained.
a few points to note for this section:
turning points/points of inflexion will be transformed to
x-intercepts (when dy/dx = 0)
positive gradient = positive graphnegative gradient = negative graph.now let's differentiate the following graph! which of the following is the y=g'(x) graph?
