Join now for JEE/NEET and also prepare for Boards Join now for JEE/NEET and also prepare for Boards. Register Now
Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
Consider a function g(x) which is defined and differentiable on (-inf, inf) and increasing in (1,2) and decreasing else where. We construct another function f (x) = g(x) - (g(x))^2+(g(x))^3 Find domain of f (x), it’s interval of monotonicity. Consider a function g(x) which is defined and differentiable on (-inf, inf) and increasing in (1,2) and decreasing else where. We construct another function f (x) = g(x) - (g(x))^2+(g(x))^3 Find domain of f (x), it’s interval of monotonicity.
f(x) = g(x) - (g(x))^2 + (g(x))^3f'(x) = g'(x) ( 1 - 2 g(x) + 3g(x)^2)Now, 3g(x)^2 - 2g(x) + 1 has Discriminant = 0. Hence, this means that this is either always positive or always negative.g'(x) > 0 in the interval (1,2)g'(x) < 0 in the interval (-8,1) U (2,8)The domain of f(x) is same as that of g(x) which is (-8,8).For the interval of monotonicity are :We cannot clearly say that 3g(x)^2 - 2g(x) + 1 is positive or negative as we do not know much about g(x). Say it is positive. Hence,f(x) is monotonically increasing in interval (1,2)f(x) is monotically decreasing in interval (-8,1) U (2,8)ThanksBharat BajajIIT Delhiaskiitians faculty
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -