Use any method to find the slope of the tangent line to the graph of the function $f ( x ) = \frac { 1 } { x ^ { 2 } }$ at the point that has x-coordinate $x = 5$ .
A)-125
B) 25
C) $\frac { 1 } { 25 }$
D) $- \frac { 2 } { 125 }$
E) $\frac { 1 } { 125 }$

Question

Use any method to find the slope of the tangent line to the graph of the function $f ( x ) = \frac { 1 } { x ^ { 2 } }$ at the point that has x-coordinate $x = 5$ .  
A)-125
B) 25
C) $\frac { 1 } { 25 }$
D) $- \frac { 2 } { 125 }$
E) $\frac { 1 } { 125 }$

Quizplus · Accepted Answer

To find the slope of the tangent line to the graph of $f(x) = \frac{1}{x^2}$ at $x = 5$, we differentiate $f(x)$ with respect to $x$ to get $f'(x) = -\frac{2}{x^3}$. Substituting $x = 5$ into $f'(x)$ gives $f'(5) = -\frac{2}{5^3} = -\frac{2}{125}$.

Use Any Method to Find the Slope of the Tangent f(x)=1x2f ( x ) = \frac { 1 } { x ^ { 2 } }f(x)=x21​

Use Any Method to Find the Slope of the Tangent $f ( x ) = \frac { 1 } { x ^ { 2 } }$