4 votes 4 votes Suppose that the derivative of a function $h$ is given by:$$h^{\prime}(x)=x(x-1)^{2}(x-2)$$On what interval(s) is $h$ increasing? $(-\infty, 0)$ $(-\infty, 0)$ and $(2, \infty)$ $(0,2)$ $(0,1)$ and $(2, \infty)$ Calculus goclasses2024-calculus-1 goclasses calculus differentiation 1-mark + – GO Classes asked Aug 28, 2022 • edited Apr 29, 2023 by Lakshman Bhaiya GO Classes 579 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes $h’(x)$ is positive in interval $(-\infty, 0)$ and $(2, \infty)$ hence $h(x)$ is increasing function in these intervals. GO Classes answered Aug 28, 2022 • edited Aug 29, 2022 by Lakshman Bhaiya GO Classes comment Share Follow See all 3 Comments See all 3 3 Comments reply sarthakdarji commented Jun 24, 2023 reply Follow Share not able to clearly understand this line representation. Can you provide the video soution of such example? 2 votes 2 votes amitarp818 commented Dec 14, 2023 reply Follow Share @sarthakdarjiWe define the increasing and decreasing intervals using the first derivative of the function f(x) as:If f'(x) ≥ 0 on an interval I, then I is said to be an increasing interval.If f'(x) ≤ 0 on an interval I, then I is said to be a decreasing interval.The function is constant in an interval if f'(x) = 0 through that interval. 1 votes 1 votes Lucky1900 commented Jan 23 reply Follow Share how did you decide +, – on that number line 0 votes 0 votes Please log in or register to add a comment.
