APFIVE In an experiment, a student records the temperature of a chemical reaction, which is modeled by a function f(t), where t is the time in seconds. To estimate the instantaneous rate of change at t = 2 seconds, the student calculates the difference quotient $$\frac{f(2) - f(2+h)}{h}$$ for a small value of h. Which of the following identifies the mistake in the student’s procedure?
The student’s method mistakenly assumes that the derivative exists even if the function is discontinuous, which is not justified.
The student reversed the order of subtraction in the difference quotient; the proper form is $$\frac{f(2+h)-f(2)}{h}$$, which would yield the correct derivative.
The student incorrectly believes that the difference quotient gives an exact value rather than an approximation, even though the method itself is valid.
The student chose a value of h that was too small, resulting in a rounding error that invalidates the limit process.
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