Find the largest open interval where the function is changing as requested.
-Decreasing $\mathrm { f } ( \mathrm { x } ) = \sqrt { 4 - \mathrm { x } }$
A) $( 4 , \infty )$
B) $( - \infty , 4 )$
C) $( - \infty , - 4 )$
D) $( - 4 , \infty )$

Question

Quizplus · Accepted Answer

To find where the function is decreasing, we need to look for intervals where the derivative is negative. 
$$\frac{d}{dx} \sqrt{4-x} = \frac{-1}{2\sqrt{4-x}}$$
The derivative is negative when the denominator is positive, which is equivalent to $4-x>0$ or $x<4$. Thus, the function is decreasing on the interval $(-\infty, 4)$.

Find the Largest Open Interval Where the Function Is Changing f(x)=4−x\mathrm { f } ( \mathrm { x } ) = \sqrt { 4 - \mathrm { x } }f(x)=4−x​

Find the Largest Open Interval Where the Function Is Changing $\mathrm { f } ( \mathrm { x } ) = \sqrt { 4 - \mathrm { x } }$