Differentiate the function and find the slope of the tangent line at the given value of the independent variable.
-$$f ( x ) = 7 x + \frac { 3 } { x } , x = 9$$
A) $\frac { 188 } { 27 }$
B) $\frac { 190 } { 27 }$
C) $\frac { 190 } { 3 }$
D) $\frac { 188 } { 3 }$

Question

Quizplus · Accepted Answer

The derivative of $f(x) = 7x + \frac{3}{x}$ is $f'(x) = 7 - \frac{3}{x^2}$. Substituting $x = 9$ into the derivative gives $f'(9) = 7 - \frac{3}{81} = 7 - \frac{1}{27} = \frac{188}{27}$, which is the slope of the tangent line at $x = 9$.

Differentiate the Function and Find the Slope of the Tangent f(x)=7x+3x,x=9f ( x ) = 7 x + \frac { 3 } { x } , x = 9f(x)=7x+x3​,x=9

Differentiate the Function and Find the Slope of the Tangent $f ( x ) = 7 x + \frac { 3 } { x } , x = 9$