Question

The limit represents f '(c) for a function f(x) and a number c. Find f(x) and c.

Answer 1

Given,

The expression of f'(c) is,

`f^(\prime)(c)=\lim _(x\rightarrow36)\frac{9\sqrt[]{x}-54}{x-36}`

As known that,

The formual of calculating the f'(c) is,

`f^(\prime)(c)=\lim _(x\rightarrow c)(f(x)-f(c))/(x-c)`

Comparing the formual with the given expression then it obtains,

`\begin{gathered} f(x)=9\sqrt[]{x} \\ f(c)=54 \\ c=36 \end{gathered}`

Hence, the expression of function f(x) is 9 sqrt(x) and the value of c is 36.