Determine where the function is increasing and where it is decreasing.
-$$f ( x ) = x ^ { 2 } - 4 x + 3$$
A) increasing on $( - 1 , \infty )$
decreasing on $( - \infty , - 1 )$

B) increasing on $( - \infty , - 1 )$
decreasing on $( - 1 , \infty )$

C) increasing on $( - \infty , 2 )$
decreasing on $( 2 , \infty )$

D) increasing on $( 2 , \infty )$
decreasing on $( - \infty , 2 )$

Question

Determine where the function is increasing and where it is decreasing.
-$$f ( x ) = x ^ { 2 } - 4 x + 3$$
A) increasing on $( - 1 , \infty )$
 decreasing on $( - \infty , - 1 )$

B) increasing on $( - \infty , - 1 )$ 
decreasing on $( - 1 , \infty )$

C) increasing on $( - \infty , 2 )$
 decreasing on $( 2 , \infty )$

D) increasing on $( 2 , \infty )$
decreasing on $( - \infty , 2 )$

Quizplus · Accepted Answer

To determine where the function is increasing or decreasing, we find the derivative of the function $f'(x) = 2x - 4$. Setting the derivative equal to zero gives $2x - 4 = 0$, solving for $x$ gives $x = 2$. This is the critical point. To the left of $x = 2$, the derivative is negative (indicating the function is decreasing), and to the right of $x = 2$, the derivative is positive (indicating the function is increasing). Therefore, the function is increasing on $(2, \infty)$ and decreasing on $(- \infty, 2)$.

Determine Where the Function Is Increasing and Where It Is f(x)=x2−4x+3f ( x ) = x ^ { 2 } - 4 x + 3f(x)=x2−4x+3

Determine Where the Function Is Increasing and Where It Is $f ( x ) = x ^ { 2 } - 4 x + 3$