91Ó°ÊÓ

True or false? Give an explanation for your answer. By definition, the instantaneous velocity of an object equals a difference quotient.

Are the statements in Problems true or false? Give an explanation for your answer. A function which is monotonic on an interval is either increasing or decreasing on the interval.

Use algebra to evaluate the limits.$$\lim _{h \rightarrow 0} \frac{1 / \sqrt{4+h}-1 / 2}{h}$$.

Are the statements in Problems true or false? Give an explanation for your answer. The function \(f(x)=x^{3}\) is monotonic on any interval.

Give an explanation for your answer. If \(f(t)\) is the quantity in grams of a chemical produced after \(t\) minutes and \(g(t)\) is the same quantity in kilograms, then \(f^{\prime}(t)=1000 g^{\prime}(t).\)

Are the statements in Problems true or false? Give an explanation for your answer. The function \(f(x)=x^{2}\) is monotonic on any interval.

Give an explanation for your answer. If \(f(t)\) is the quantity in kilograms of a chemical produced after \(t\) minutes and \(g(t)\) is the quantity in kilograms produced after \(t\) seconds, then \(f^{\prime}(t)=60 g^{\prime}(t).\)

Find the derivatives algebraically. $$f(x)=5 x^{2}\( at \)x=10$$

Find the derivatives algebraically. $$f(x)=x^{3}\( at \)x=-2$$

Assume \(g(v)\) is the fuel efficiency, in miles per gallon, of a car going at a speed of \(v\) miles per hour. What are the units of \(g^{\prime}(v)=\frac{d g}{d v} ?\) There may be more than one option. (a) (miles) \(^{2} /(\text { gal })(\text { hour })\) (b) hour/gal (c) gal/hour (d) (gal)(hour)/(miles) \(^{2}\) (e) (miles/gallon)/(miles/hour)