Find the largest open interval where the function is changing as requested.
-Increasing $\mathrm { f } ( \mathrm { x } ) = \frac { 1 } { 4 } \mathrm { x } ^ { 2 } - \frac { 1 } { 2 } \mathrm { x }$
A) $( - \infty , - 1 )$
B) $( - \infty , \infty )$
C) $( 1 , \infty )$
D) $( - 1,1 )$

Question

Quizplus · Accepted Answer

We can take the derivative of the function to see when it is increasing or decreasing:

$\mathrm { f' } ( \mathrm { x } ) = \frac { 1 } { 2 } \mathrm { x } - \frac { 1 } { 2 }$

To find when the function is increasing, we need to find when the derivative is positive:

$\frac { 1 } { 2 } \mathrm { x } - \frac { 1 } { 2 } > 0$

$\mathrm { x } > 1$

Therefore, the largest open interval where the function is increasing is $(1,\infty)$.

Find the Largest Open Interval Where the Function Is Changing f(x)=14x2−12x\mathrm { f } ( \mathrm { x } ) = \frac { 1 } { 4 } \mathrm { x } ^ { 2 } - \frac { 1 } { 2 } \mathrm { x }f(x)=41​x2−21​x

Find the Largest Open Interval Where the Function Is Changing $\mathrm { f } ( \mathrm { x } ) = \frac { 1 } { 4 } \mathrm { x } ^ { 2 } - \frac { 1 } { 2 } \mathrm { x }$