the value of

Given: $f(x)=x^{2}$

find: $\frac{f(5)-f(1)}{(5-1)} \ldots$ (i)

Firstly, we find the f(5)

Putting the value of x = 5 in the given eq., we get

$f(5)=(5)^{2}$

$\Rightarrow f(5)=25$

Similarly,

$f(1)=(1)^{2}$

$\Rightarrow f(1)=1$

Putting the value of f(5) and f(1) in eq. (i), we get

$\frac{\mathrm{f}(5)-\mathrm{f}(1)}{(5-1)}=\frac{25-1}{5-1}=\frac{24}{4}=6$

Hence, the value of $\frac{\mathrm{f}(5)-\mathrm{f}(1)}{(5-1)}=6$