미분 전체 문제

T/F: The definition of the derivative of a function at a point involves taking a limit.

In your own words, explain the difference between the average rate of change and instantaneous rate of change.

Let $y=f(x)$. Give three different notations equivalent to “$f\,'(x)$.”

If two lines are perpendicular, what is true of their slopes?

What is the instantaneous rate of change of position called?

Given a function $y=f(x)$, in your own words describe how to find the units of $f\,'(x)$.

What functions have a constant rate of change?

What is the name of the rule which states that $\displaystyle \frac{d}{dx}\big(x^n\big) = nx^{n-1}$, where $n>0$ is an integer?

What is $\displaystyle \frac{d}{dx}\big(\ln x\big)$?

Give an example of a function $f(x)$ where $f\,'(x) = f(x)$.

Give an example of a function $f(x)$ where $f\,'(x) = 0$.

The derivative rules introduced in this section explain how to compute the derivative of which of the following functions?

• $\displaystyle f(x) = \frac{3}{x^2}$

• $g(x) = 3x^2-x+17$

• $h(x) = 5\ln x$

• $j(x) = \sin x \cos x$

• $k(x) = e^{x^2}$

• $m(x) = \sqrt{x}$

Explain in your own words how to find the third derivative of a function $f(x)$.

Give an example of a function where $f\,'(x) \neq 0$ and $f\,''(x) = 0$.

Explain in your own words what the second derivative “means.”

If $f(x)$ describes a position function, then $f\,'(x)$ describes what kind of function? What kind of function is $f\,''(x)$?

Let $f(x)$ be a function measured in pounds, where $x$ is measured in feet. What are the units of $f\,''(x)$?

Describe what an “extreme value” of a function is in your own words.

Sketch the graph of a function $f$ on $(-1,1)$ that has both a maximum and minimum value.

Describe the difference between absolute and relative maxima in your own words.