$\text { Find the derivative of the function } g ( x ) = - 2 \text { by the limit process. }$
A) $g ^ { t } ( x ) = 2$
B) $g ^ { t} ( x ) = 2 x$
C) $g ^ { t } ( x ) = - 2 x$
D) $g ^ { t } ( x ) = 0$
E) $g ^ { t } ( x ) = - 2$

Question

$\text { Find the derivative of the function } g ( x ) = - 2 \text { by the limit process. }$ 
A) $g ^ { t } ( x ) = 2$
B) $g ^ { t} ( x ) = 2 x$
C) $g ^ { t } ( x ) = - 2 x$
D) $g ^ { t } ( x ) = 0$
E) $g ^ { t } ( x ) = - 2$

Quizplus · Accepted Answer

Since the function is constant, its derivative is zero. This can be shown through the limit definition of a derivative:

$$g'(x) = \lim_{h	o 0} \frac{g(x+h) - g(x)}{h} = \lim_{h	o 0} \frac{-2 - (-2)}{h} = \lim_{h	o 0} 0 = 0$$

Therefore, the correct answer is D.

Find the derivative of the function g(x)=−2 by the limit process. \text { Find the derivative of the function } g ( x ) = - 2 \text { by the limit process. } Find the derivative of the function g(x)=−2 by the limit process.

$\text { Find the derivative of the function } g ( x ) = - 2 \text { by the limit process. }$