question 8\nto determine the interval(s) where a function is increasing, we find the interval(s) or point(s)…

question 8\nto determine the interval(s) where a function is increasing, we find the interval(s) or point(s) where\nthe derivative is undefined.\nthe derivative is positive.\nthe derivative is negative.\nno correct answer choice is given.\nthe derivative is zero.

question 8\nto determine the interval(s) where a function is increasing, we find the interval(s) or point(s) where\nthe derivative is undefined.\nthe derivative is positive.\nthe derivative is negative.\nno correct answer choice is given.\nthe derivative is zero.

Answer

Brief Explanations:

According to the first - derivative test in calculus, if (y = f(x)) is a differentiable function, then (f(x)) is increasing on an interval (I) if (f^{\prime}(x)>0) for all (x\in I). When the derivative is undefined, it may be a point of non - differentiability (e.g., a corner or a vertical tangent), but this does not directly tell us about where the function is increasing. When the derivative is negative, the function is decreasing. When the derivative is zero, the function has a critical point (it could be a local maximum, local minimum, or an inflection point if the second - derivative test is considered further), but not a point of increase.

Answer:

the derivative is positive.