Mathematics - Functions Question with Solution | TestHub

$f^{\prime }(5)={\lim }_{h\to 0}\frac{f(5+h)-f(5)}{h}$ $={\lim }_{h\to 0}\frac{f(5+h)-f(5+0)}{h}$ $={\lim }_{h\to 0}\frac{f(5)\cdot f(h)-f(5)+f(0)}{h}$ $(\because f(x+y)=f(x),f(y)$ for all $x,y)$ $=\left({\lim }_{h\to 0}\frac{f(h)-f(0)}{h}\right)\cdot f(5)=f^{\prime }(0)\cdot f(5)$ $=3\times 2=6$