SOLUTION 4: Begin with the function
$$f(x)= x^{3/4}$$
and choose
$$x-values: 16 \rightarrow 14$$
so that
$$\Delta x = 14-16 = -2$$
The derivative of $\ y=f(x) \$ is
$$f'(x)= \displaystyle{ 3 \over 4 }x^{-1/4} = \displaystyle{ 3 \over 4 x^{1/4} }$$
The exact change of $y-$values is
$$\Delta y = f(14) - f(16)$$ $$= 14^{3/4} - 16^{3/4}$$ $$= 14^{3/4} - (16^{1/4})^3$$ $$= 14^{3/4} - (2)^3$$ $$= 14^{3/4} - 8$$
The Differential is
$$dy = f'(16) \ \Delta x$$ $$= \displaystyle{ 3 \over 4 (16)^{1/4} } \cdot (-2)$$ $$= \displaystyle{ 3 \over 4 (2) } (-2)$$ $$= \displaystyle{ 3 \over 8 } (-2)$$ $$= \displaystyle{ -3 \over 4 }$$ $$= \displaystyle{ -0.75 }$$
We will assume that
$$\Delta y \approx dy \ \ \ \ \longrightarrow$$ $$14^{3/4} - 8 \approx -0.75 \ \ \ \ \longrightarrow$$ $$14^{3/4} \approx 8-0.75 \ \ \ \ \longrightarrow$$ $$14^{3/4} \approx 7.25$$

NOTE: The number 16 was chosen for its proximity to 14 and for it's convenient fourth root. Check the accuracy of the final estimate using a CALCULATOR: $14^{3/4} \approx 7.2376$