What does differentiation actually mean?
Differentiation is defined as the rate of change of a function. Imagine we had a function f(x), which we shall let equal x2. We all know what the graph of x2 looks like.
The derivative of x2 is 2x. This means that, as the variable x increases, the gradient increases by 2x. In graphing a derivative, effectively the gradient is on the y axis, hence the steeper the curve of y, the higher the derivative.
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Related Maths IB answers
All answers ▸Two functions, y1 & y2, are given by y1=x^2+16x+4; y2=2(3x+2). Find analytically the volume of the solid created by revolving the area between the two curves by 2pi radians around the x-axis. N.B. y2>y1 on the interval between the points of intersection.
Can you explain the approach to solving IB maths induction questions?
Let f (x) = 5x and g(x) = x2 + 1 , for x ∈ . (a) Find f-1(x) . (b) Find ( f ° g) (7) .
Find a and b (both real) when (a+b*i)^2=i.