Question

F(x)= x^3+3x^2+2x+1 using only the definition of derivatives, find f prime of x

Answer 1

\[f'(x)=\lim_{\Delta x \rightarrow 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}\]

Answer 2

Yeah but how to you plug that in to the equation?

Answer 3

If you are a little too intimidated by \(\Delta x\), then use \(h\).\[f'(x) = \lim_{h \to 0 } {f(x + h) - f(x) \over h}\]Essentially, they mean the same thing.

Answer 4

That's the equation I use but I don't know what to put in the box for (x+h)

Answer 5

You can plug it in very easily. To start with,\[f(x + h) = (x + h)^3 + 3(x + h)^2 + 2(x + h) + 1\]If you have learnt about functions, then you'd understand the above easily.