# Differentiation Short Questions (Question 11 – 14)

Question 11:
Given that the graph of function $f\left(x\right)=h{x}^{3}+\frac{k}{{x}^{2}}$  has a gradient function $f‘\left(x\right)=12{x}^{2}-\frac{258}{{x}^{3}}$ such that h and kare constants. Find the values of and k.

Solution:

Question 12:

Solution:

Question 13:

Solution:

Question 14:
Given y = x (6 – x), express $y\frac{{d}^{2}y}{d{x}^{2}}+x\frac{dy}{dx}+18$ in terms of xin the simplest form.

Hence, find the value of xwhich satisfies the equation  $y\frac{{d}^{2}y}{d{x}^{2}}+x\frac{dy}{dx}+18=0$

Solution: