\text { (a) } f \text { is continuous for } x \geq 0 \text {, } \text { (b) } f^{\prime}(x) \text { exists for } x>0 \text {,

} \text { (c) } f(0)=0 \text { (d) } f^{\prime} \text { is monotonically increasing. } g(x)=\frac{f(x)}{x} \quad(x>0) and prove that g is monotonically increasing.