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.
TT
Related Maths IB answers
All answers ▸Having x(x+4)=y, calculate dy/dx
Given two functions f and g where f(x)=3x-5 and g(x)=x-2. Find: a) the inverse f^-1(x), b) given g^-1(x)=x+2, find (g^-1 o f)(x), c) given also that (f^-1 o g)(x)=(x+3)/3, solve (f^-1 o g)(x)=(g^-1 o f)(x)
A sequence of numbers have the property that x, 12, y, where x > 0, y > 0, form a geometric sequence while 12, x, 3y form an arithmetic sequence. A)If xy = k, find k. B)Find the value of x and y.
What does a derivative mean and why does setting it equal to zero allow us to find the minima/maxima of a function