Given,
The expression of f'(c) is,
[tex]f^{\prime}(c)=\lim _{x\rightarrow36}\frac{9\sqrt[]{x}-54}{x-36}[/tex]
As known that,
The formual of calculating the f'(c) is,
[tex]f^{\prime}(c)=\lim _{x\rightarrow c}\frac{f(x)-f(c)}{x-c}[/tex]
Comparing the formual with the given expression then it obtains,
[tex]\begin{gathered} f(x)=9\sqrt[]{x} \\ f(c)=54 \\ c=36 \end{gathered}[/tex]
Hence, the expression of function f(x) is 9 sqrt(x) and the value of c is 36.
