Question

I have no idea how to solve this. Can someone please help me for a medal? :)
(posting below)

Answer 1

\[\frac{ f(x+Δx)−f(x) }{ Δx }\]

if f(x) = x^2

Answer 2

compute as \(\huge \frac{(x + \Delta x)^2 - x^2}{\Delta x}\)

Answer 3

so expand out the \(\large (x + \Delta x)^2\) in the numerator :p

Answer 4

I know how to get to the expanding part, but I am not sure how to expand the numerator.
Could you show me how?

Answer 5

Would it end up looking like this...
\[\frac{ x^{2} + Δx^{2}-x^{2} }{ Δx } \]

Answer 6

first expand out \( (x+Δx)^2\) on its own

that's \( (x+Δx) \times (x+Δx)\)