Question

Find the largest open interval where the function is increasing. correct answer will get brainliest

Answer 1

Answer:

Correct answer: C.  (1,∞)

Step-by-step explanation:

First Derivative

Given a real continuous function f(x), the first derivative f'(x) represents the slope of the tangent line for any value of x.

If the slope of the line is positive, then the function is increasing, if the slope of the line is negative, the function is decreasing.

The function to analyze is:

$f(x)=x^2-2x+1$

Computing the first derivative:

$f'(x)=2x-2$

The function will be increasing when:

$2x-2>0$

Dividing by 2:

$x-1>0$

Solving:

x > 1

This solution is represented by the interval (1,∞)

Correct answer: C.  (1,∞)