APFIVE Experimental Procedure: A student conducts an experiment to measure the instantaneous rate of temperature change during a chemical reaction. The student records temperature readings at regular intervals and then chooses t = 2 seconds to compute the derivative of the temperature function f(t). To approximate f′(2), the student sets up the difference quotient as $$\frac{f(2) - f(2+h)}{h}$$ for a small h. Based on this procedure, what is the mistake in the student’s approach?
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’s method mistakenly assumes that the derivative exists even if the function is discontinuous, which is not justified.
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.
Question Leaderboard
Not enough data yet to show leaderboard.