Applying the Mean Value Theorem

In the context of the Mean Value Theorem, let $f(x)=\sqrt{x^2+9}-\frac{1}{x+2}$ on the closed interval $[1,4]$. The theorem guarantees that there exists a number c in (1,4) such that

$f'(c)=\frac{f(4)-f(1)}{4-1}.$

Solve the equation $f'(c)=\frac{f(4)-f(1)}{3}$ to determine, approximately, the value of c.