a positive, D negative, so mod not required value under [ ] is 0 at 1/2 (where dy/dx is 0) so the answer is 3/4 at x=1/2 now let me watch the video and confirm 😊
The domain of f(x) is all real numbers and satisfies f(x + 1) = 2f(x) For x ∈ (0,1], f(x) = x(x - 1) For values x ∈ (-infinity, m], f(x) >= - 8/9 What is the value of m? Sir provide the solution of this question
I'm 44 yrs old but enjoy your videos... I solve them mentally in seconds ... then watch the video and get amazed how exactly you do the same thing on board...
@@engineergaming9755 learn to draw the graphs and correlate the concepts like domain, range, continuity, differntiabylity, limits, etc on graphs. Try to understand why dy/dx is slope and integral is area under the curve. What 2nd and 3rd derivative signifies on graph. How maxima and minima arw related to 2nd derivative ... again on graph etc. btw, i was taught calculus by vinay malhotra (allahabad) in late 90s while preparing for JEE... he was a great teacher and calculus was my favorite topic... hence the result. in short, find a good teacher (just like the one who make these videos) and work hard along with the teacher
@@engineergaming9755 Not required ,When f'(x)=0 it is either a minima or maxima ,no other points in the function within that interval satisfy that condition(because if it did f'(X) would also be 0 there).So that along with endpoints because the absolute maximum/min can also lie on the endpoints and which can easily be checked by just plugging in the values.
There seems to be an error in the last part , k>=-1 means all solutions satisfy in the options . It should be other way around -1>=k . The Left hand limit at -1 is k+2 ,the value at f(-1) is k+2 and the right hand limit is actually 1 . So for local minima at -1 the RHL should always be higher than f(-1) which means 1>=k+2 and that means -1>=k . the LHL should also be >=f(-1) but that is true for all k . Which means the only possible value of k from the options is -1 . Again note if question was multiple choice and any value <-1 was in the options they all would be correct
