Question

let f(x)=sqrt2x. If the rate of change of f at x = c is four times its rate of change at x=1, then c =?

Answer 1

\(\large{\begin{array}{llll}
f(x)=\sqrt{2x}\qquad &x=1\qquad {\color{blue}{ f(1)}}=\sqrt{2(1)}\implies {\color{blue}{ \sqrt{2}}}
\\ \quad \\
&x=c\qquad f(c)=4\cdot {\color{blue}{ f(1)}}\implies 4{\color{blue}{ \sqrt{2}}}
\end{array}
\\ \quad \\\\ \quad \\
\textit{rate of change}=\cfrac{f(c)-f(1)}{c-1}}\)

solve for "c"