Question

f(x)=2x(f(x+Δx)-f(x))/Δx

Transformations of functions
ANSWERED
asked 2021-06-13

\(\displaystyle{f{{\left({x}\right)}}}={2}{x}\)
\(\displaystyle\frac{{ f{{\left({x}+\triangle{x}\right)}}- f{{\left({x}\right)}}}}{\triangle}{x}\)

Answers (1)

2021-06-14

Using the given function, substitute to the difference quotient and simplify: \((f(x+\triangle x)-f(x))/\triangle x=(2(x+\triangle x)-2x)/\triangle x\\ \displaystyle=\frac{{{2}{x}+{2}\triangle{x}-{2}{x}}}{\triangle}{x}\\ \displaystyle={2}\triangle\frac{x}{\triangle}{x}\\ =2\)

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