Applications of Derivatives flashcards

Question 1

What is a critical point of a function $f$?

Accepted Answer

A point $x=c$ in the domain of $f$ where $f'(c)=0$ or $f'(c)$ does not exist. (Critical point refers to the $x$-value; the corresponding graph point is $(c,f(c))$.)

Question 2

Apply the Second Derivative Test: $f'(c)=0$ and $f''(c)=-5$. What occurs at $x=c$?

Accepted Answer

Since $f''(c)<0$, $f$ has a local maximum at $x=c$.

Question 3

What is the standard strategy for related rates problems?

Accepted Answer

Relate variables with an equation, differentiate implicitly with respect to time $t$, substitute known values at the instant, then solve for the desired rate (e.g., use $\frac{dx}{dt}$, $\frac{dy}{dt}$).

Applications of Derivatives flashcards

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