4 votes 4 votes It should be 1 and 3 ?? please correct me if I'm wrong. Calculus engineering-mathematics calculus + – Ashwin Kulkarni asked Jan 1, 2018 Ashwin Kulkarni 1.2k views answer comment Share Follow See all 20 Comments See all 20 20 Comments reply joshi_nitish commented Jan 1, 2018 reply Follow Share yes, you are correct. 1 votes 1 votes Anu007 commented Jan 1, 2018 reply Follow Share why you think about 3rd. i think 1st only 0 votes 0 votes joshi_nitish commented Jan 1, 2018 reply Follow Share because $\frac{dy}{dx}<0$ for x<3 1 votes 1 votes Manu Thakur commented Jan 1, 2018 reply Follow Share yes i is only correct keep x=1 and x=-1, 3rd is wrong. 0 votes 0 votes Anu007 commented Jan 1, 2018 reply Follow Share Nitish can you point out how to check increasing or decreasing. 0 votes 0 votes Manu Thakur commented Jan 1, 2018 reply Follow Share @anu isn't the counter example correct, which i mentioned? 0 votes 0 votes Manu Thakur commented Jan 1, 2018 reply Follow Share anyway, for negative values which are obviously less than 3, this function will keep on increasing. 0 votes 0 votes hacker16 commented Jan 1, 2018 reply Follow Share 1 and 3 both are correct. 0 votes 0 votes Manu Thakur commented Jan 1, 2018 reply Follow Share @hacker16 how? did you consider my comments? 0 votes 0 votes joshi_nitish commented Jan 1, 2018 reply Follow Share see this, 2 votes 2 votes hacker16 commented Jan 1, 2018 reply Follow Share f'(x) < 0 on (-∞, 3), thus f(x) is decreasing f'(x) > 0 on (3, ∞), thus f(x) is increasing 1 votes 1 votes hacker16 commented Jan 1, 2018 reply Follow Share @manu check nitish comment it will clarify everything. 0 votes 0 votes joshi_nitish commented Jan 1, 2018 reply Follow Share @Anu sir, if $\frac{dy}{dx}$ > 0 then function is increasing if $\frac{dy}{dx}$ < 0 then function is decreasing if $\frac{dy}{dx}$ = 0 then function is constant 4 votes 4 votes Manu Thakur commented Jan 1, 2018 reply Follow Share yep, my reasoning was incorrect. A function f(x) is said to be strictly decreasing on an interval I if f(b)<f(a) for all b>a. function for larger values, gives the smaller result. I am not so good in maths specially with these graphs. 1 votes 1 votes srestha commented Jan 1, 2018 reply Follow Share But if we find pointwise f(5)=25-30+666=661 f(4)=658 ----------------------------------------------------------- Now again f(2)=658 f(1)=661 f(0)=666 f(-1)=673 So, cannot we tell , it is only increasing function? Moreover, we get slope, where there is two values x and y But we are here calculating only one value of x. Where am I mistaking? 0 votes 0 votes Manu Thakur commented Jan 1, 2018 reply Follow Share @srestha f(2) = 658 f(1)=661 f(0)=666 f(-1)=673 see here on larger value of x, function f(x) is giving smaller value. see the definition of decreasing function in the above comment by me. 0 votes 0 votes hacker16 commented Jan 1, 2018 reply Follow Share @srestha you need to start checking from left side of the number system while checking for increasing or decreasing, here also from negative infinity to +3, it is definitely decreasing. also in f(b)-f(a)/b-a ,put the b and a appropriately and you will get the right answer 0 votes 0 votes Anjan commented Jan 1, 2018 reply Follow Share $f(x) = x^2 - 6x + 666$ $f'(x) = 2x-6$ 1) Find critical points, here $3$ is critical point. 2) find sign in the intervals $(-\infty,3),(3, \infty)$ 3) take any values say x=1 in $(-\infty,3)$ then $f'(x)$ is -ve function is decreasing 4) take any values say x=4 in $(3,\infty)$ then $f'(x)$ is +ve function is increasing. 1 votes 1 votes srestha commented Jan 1, 2018 reply Follow Share yes a) and c) both correct 1 votes 1 votes Shubhanshu commented Jan 7, 2018 reply Follow Share Yes, I think both a and c are correct. 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes it will be easy by solving through wavey curve a,c are the correct options shuham kumar answered Sep 20, 2022 shuham kumar comment Share Follow See all 0 reply Please log in or register to add a comment.