Select all the statements that are true about net change. The net change of displacement is equal to the integral of velocity. The marginal (derivative of) cost of producing $x$ units is given by the expression $250 x^{3}-5800 x+21100$. The cost of increasing production from 20 to 30 is given by the expression $\int_{20}^{30}\left(750 x^{2}-5800\right) d x$. The net change of a function $f$ over an interval is equal to the integral of $f^{\prime}$ evaluated at the endpoints of the interval. If the flow rate of the number of subway passengers per hour from $t_{1}$ to $t_{2}$ is represented by the function $f$, then the number of people using the subway between time $t_{1}$ and $t_{2}$ is $\int_{t_{1}}^{t_{2}} f^{\prime}(x) d x$.
Solution
Step 1 ：Evaluate each statement about net change.
Step 2 ：The first statement is true: The net change of displacement is equal to the integral of velocity.
Step 3 ：The second statement is false: The cost of increasing production from 20 to 30 units should be given by the integral of the marginal cost function from 20 to 30, not by the expression provided.
Step 4 ：The third statement is true: The net change of a function over an interval is indeed equal to the integral of its derivative evaluated at the endpoints of the interval.
Step 5 ：The fourth statement is false: The number of people using the subway between time $t_{1}$ and $t_{2}$ should be given by the integral of the flow rate function from $t_{1}$ to $t_{2}$, not by the integral of its derivative.
Step 6 ：Final Answer: \(\boxed{\text{The true statements are: 'The net change of displacement is equal to the integral of velocity' and 'The net change of a function f over an interval is equal to the integral of f' evaluated at the endpoints of the interval.'}}\)
