Equation e^x-cx^2 has three real roots, then the derivative of function f(x) = e^x-cx^2 must have two real roots as between two roots of the equation there exists atleast one root of its derivative. Now f'(x) = e^x - 2cx. Now graph of y = e^x and y = 2cx must intersect at two distinct points. First we find the value of c for which graph touch. For that e^x = 2c (comparing derivatives i.e. slopes). y = 2c and x = 1. So, y = e. i.e. point of contact of line y = 2cx and y = e^x is (1, e), for which 2c = e Thus line y =2cx, touches y = e^x when slope of the line is e. Now if line cuts y = e^x at two distinct points then slope of the line must be more than e, i.e. 2c > e or c > e/2. So, least integral value of c is 2.
Crystal clear
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Sir cengage book ke author aap hi ho 🙏 pls reply
Yes
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Sir I have cengage of yours of 2012 edition ...is it ok to solve it or shall I purchase the new 2019 one...Plz tell sir
Its alright
U got [NIT]?
@@busyhacker3286 yes brother!
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Sir pls continue continuity and differentiability topics
Respected sir where u will take physical classes and awesome video
I got many things from this video
Sir plz make videos on jee advanced 2020
Please discuss the chapter in details drawing the graph sir
Sirji next video on questions?
Great sir 😊
Upload more discussion.
Why one one ness of the function inside the box is necessary??
Sir please make more videos
Sir ur concepts are awesome
Sir, why you stop posting videos, if you only post videos on good conceptual questions, it will be of great help.
Upload video on drawing composite function pls 😊
Vv ausome
What was the prime region to define this type of function.Is it exists in our nature.If yes Please give an example.??????
You can visualise the situation of going up the steps where exactly matches it
sir u r great..................
Sir where I can get your lectures
Sir countinety ka video or daliya sir
if e^x=cx^2 has three real solutions what is the smallest positive integral value of c sir please give the solution
Equation e^x-cx^2 has three real roots, then the derivative of function f(x) = e^x-cx^2 must have two real roots as between two roots of the equation there exists atleast one root of its derivative. Now f'(x) = e^x - 2cx. Now graph of y = e^x and y = 2cx must intersect at two distinct points. First we find the value of c for which graph touch. For that e^x = 2c (comparing derivatives i.e. slopes). y = 2c and x = 1. So, y = e. i.e. point of contact of line y = 2cx and y = e^x is (1, e), for which 2c = e Thus line y =2cx, touches y = e^x when slope of the line is e. Now if line cuts y = e^x at two distinct points then slope of the line must be more than e, i.e. 2c > e or c > e/2. So, least integral value of c is 2.
@pritam Mishra did u get into dse
Superb sir
sir vedio kam se kam ek ghante ki kato....
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