I know how to approximate the value of a function by (a) plugging in values and (b) using a linear approximation, i.e. $\displaystyle f(x)\approx f(a)+f'(a)(x-a)$

But, how would one approximate thechangein a function, i.e. $\displaystyle \Delta y$ of $\displaystyle y=30z+50z^2+40z^3$ when $\displaystyle z$ changes from 0.90 to 0.92 by using the first-order and second order derivatives?

Any insights would be much appreciated!