Ok so derivative are an expression of the rate of change of a function. Cool I get that.
– F(x) = 5 : the product of this function is always 5 there is no increase or decrease so there is no change no matter what X is and it makes sense that the derivative would equal 0.
– F(x) = 5x : it is obvious that each time x increases by 1 the product of this function increases by 5. I get it.
– F(x) = x² => F'(x) = 2x : starting from here the numbers stop matching and make me feel like I am missing something. F'(1) = 1. This makes perfect sense. F(x) did in fact increase by 1 when going from F(0) to F(1). Then I try F'(2) = 2×2 = 4. Huh ? But F(x) only increased by 3 between F(1) and F(2) ? Maybe I am looking at the rate of change as compared to F(0) ? after all there is an increase of 4 between F(0) and F(2). Let’s check with 3 then. F'(3) = 6. Wtf ?!
I don’t get it what does it mean when F'(2) = 4 ? When X = 2 then …? and what does it tell me about the original function. Thanks and hope my english isn’t too awfull.
In: 40
> F(x) only increased by 3 between F(1) and F(2)
– F(x) increases by 3 between F(1) and F(2). The slope is 3/1 = 3.
– F(x) increases by 0.39 between F(1.9) and F(2). The slope is 0.39/0.1 = 3.9.
– F(x) increases by 0.0399 between F(1.99) and F(2). The slope is 0.0399 / 0.01 = 3.99
– F(x) increases by 0.003999 between F(1.999) and F(2). The slope is 0.003999 / 0.001 = 3.999.
As you bring the two points close together, the slope approaches 4.
Latest Answers