Question

A differentiable function $f$ is defined for all $x>0$ as $f\left(x\right)=6x+5$ then $f^{{}^{\prime }}\left(16\right)$ is equal to

• A. $64$
• B. $16$
• C. $32$
• D. $6$

Answer 1

Answer: (D)

$6$

It is given that
$f\left(x\right)=6x+5$
Differentiating with respect to $x$, gives us
$\frac{df\left(x\right)}{dx}=\frac{d(6x+5)}{dx}$
$=6$
Hence
$f^{\prime }\left(x\right)=6$
This implies that the first derivative of the function is independent of $x$.
Hence
$f^{\prime }\left(16\right)=6$.