Estimate $\left. \frac { \mathrm { d } R } { \mathrm {~d} p } \right| _ { p = 17 }$ of the function $R = \frac { 16 } { p }$ .
A) $\frac { 16 } { 289 }$
B) $- \frac { 33 } { 289 }$
C) $16$
D) $- \frac { 1 } { 289 }$
E) $- \frac { 16 } { 289 }$

Question

Estimate $\left. \frac { \mathrm { d } R } { \mathrm {~d} p } \right| _ { p = 17 }$ of the function $R = \frac { 16 } { p }$ .  
A) $\frac { 16 } { 289 }$
B) $- \frac { 33 } { 289 }$
C)   $16$
D) $- \frac { 1 } { 289 }$
E) $- \frac { 16 } { 289 }$

Quizplus · Accepted Answer

To find the derivative of $R = \frac{16}{p}$ with respect to $p$, we use the power rule. The derivative is $\frac{dR}{dp} = -16p^{-2}$. Evaluating this at $p = 17$ gives $-16(17)^{-2} = -\frac{16}{289}$.

Estimate dR dp∣p=17\left. \frac { \mathrm { d } R } { \mathrm {~d} p } \right| _ { p = 17 } dpdR​​p=17​

Estimate $\left. \frac { \mathrm { d } R } { \mathrm {~d} p } \right| _ { p = 17 }$