For the function $f ( t ) = \frac { 1 } { t }$ determine the average rate of change between the values $t = \tau$ And $t = a + h$
A) $\frac { - 1 } { a ( a + h ) }$

B) $\frac { - 2 } { h }$

C) $( 3 h + 1 )$

D) $\frac { - 1 } { ( 2 h - 1 ) }$

E) $\frac { 1 } { a ( a + h ) }$

Question

For the function $f ( t ) = \frac { 1 } { t }$ determine the average rate of change between the values $t = \tau$ And $t = a + h$
A) $\frac { - 1 } { a ( a + h ) }$

B) $\frac { - 2 } { h }$

C) $( 3 h + 1 )$

D) $\frac { - 1 } { ( 2 h - 1 ) }$

E) $\frac { 1 } { a ( a + h ) }$

Quizplus · Accepted Answer

The average rate of change between two values is given by the formula: 
$$\frac{f(a+h)-f(\tau)}{(a+h)-\tau}$$
Substituting the given values, we get:
$$\frac{\frac{1}{a+h}-\frac{1}{\tau}}{(a+h)-\tau}$$
Simplifying this expression using the common denominator $(a+h)\tau$, we get:
$$\frac{\tau-(a+h)}{a\tau(a+h)}=\frac{-h}{a\tau(a+h)}=\frac{-1}{a(a+h)}$$
Therefore, the correct answer is A.

For the Function f(t)=1tf ( t ) = \frac { 1 } { t }f(t)=t1​

For the Function $f ( t ) = \frac { 1 } { t }$