Let $f ( x ) = \sqrt { x }$ Which of the following is equal to $\lim _ { x \rightarrow 4 } \frac { f ( x ) - f ( 4 ) } { x - 4 }$ ?

A) $- \frac { 1 } { 4 }$
B) $\frac { 1 } { 4 }$
C) $- \frac { 1 } { 2 }$
D) $\frac { 1 } { 2 }$
E)Does not exist

Question

Let $f ( x ) = \sqrt { x }$ Which of the following is equal to $\lim _ { x \rightarrow 4 } \frac { f ( x ) - f ( 4 ) } { x - 4 }$ ?

A) $- \frac { 1 } { 4 }$
B) $\frac { 1 } { 4 }$
C) $- \frac { 1 } { 2 }$
D) $\frac { 1 } { 2 }$
E)Does not exist

Quizplus · Accepted Answer

This limit represents the derivative of $f(x) = \sqrt{x}$ at $x = 4$, which can be calculated using the definition of the derivative. The derivative of $\sqrt{x}$ is $\frac{1}{2\sqrt{x}}$, so at $x = 4$, the derivative is $\frac{1}{2\sqrt{4}} = \frac{1}{4}$.

Let f(x)=xf ( x ) = \sqrt { x }f(x)=x​ Which of the Following Is Equal To

Let $f ( x ) = \sqrt { x }$ Which of the Following Is Equal To