Home
Class 12
MATHS
Find the range of values of a if f(x)=2e...

Find the range of values of `a` if `f(x)=2e^x-a e^(-x)+(2a+1)x-3` is monotonically increasing for all values of `xdot`

Text Solution

Verified by Experts

f(x) =`2e^(+)+ae^(-x)+ae^(-x)+2a+1`
`=e^(-x)(2e^(2x))+(2a+1)e^(x)+a)`
`=e^(-x)(e^(x)+a)(2e^(e^(x))+1)`
For f(x) to be increasing f(x) to the increasing `f(x)ge 0 forall` x in R
`rarr e^(x)+age0forall` x in R
`rarr age-e^(x)forall` x in R
`rarr age0`
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Solved Examples|20 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercise 6.1|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

The function f(x)=e^(ax)+e^(-ax),agt0 is monotonically increasing for

Find the range of the function f(x) = (e^x - e^-x) .

Find the possible values of a such that f(x)=e^(2x)-(a+1)e^x+2x is monotonically increasing for x in Rdot

Find the values of x for which the function f(x)=x^(3)-7x^(2)+8x-10 is monotonic increasing.

Find the range of values of x for which the function f(x)=2x^(3)-9x^(2)-24 x+5 increases with x

If f(x)= x^(3) + ax^(2) + bx + c is an increasing function for all real values of x then-

The function y=2x^2-log(x) is monotonically increasing for values of x(!=0) satisfying the inequalities____ and monotonically decreasing for values of x satisfying the inequalities_____.

Find the intervals in which f(x)=(x+2) e^(-x) is increasing

If alt0 , and f(x)=e^(ax)+e^(-ax) Is monotonically decreasing. Find the interval in which x belongs.

Find all the possible values of f(x) =(1-x^2)/(x^2+3)