Find the equation of the tangent line to the graph of $f ( x ) = \frac { 3 } { x }$ at the point $\left( 4 , \frac { 3 } { 4 } \right)$ .
A) $y = \frac { 3 } { 4 } x + \frac { 3 } { 2 }$
B) $y = - \frac { 3 } { 16 } x + \frac { 3 } { 2 }$
C) $y = - \frac { 3 } { 4 } x + \frac { 3 } { 2 }$
D) $y = \frac { 3 } { 16 } x$

Question

Quizplus · Accepted Answer

To find the equation of the tangent line, first, calculate the derivative of $f(x) = \frac{3}{x}$, which gives $f'(x) = -\frac{3}{x^2}$. Evaluating this derivative at $x = 4$ gives the slope of the tangent line: $f'(4) = -\frac{3}{16}$. Using the point-slope form of a line, $y - y_1 = m(x - x_1)$, with $m = -\frac{3}{16}$ and the point $(4, \frac{3}{4})$, we find the equation of the tangent line to be $y = -\frac{3}{16}x + \frac{3}{2}$.

Find the Equation of the Tangent Line to the Graph f(x)=3xf ( x ) = \frac { 3 } { x }f(x)=x3​

Find the Equation of the Tangent Line to the Graph $f ( x ) = \frac { 3 } { x }$