Question

if f(x) = ax + cosx is strictly increasing on R find a
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Answer 1

Given info : f(x) = ax + cosx is strictly increasing on R

To find : the value of a.

solution : here function, f(x) = ax + cosx

differentiating f(x) with respect to x we get,

f'(x) = a + (-sinx) = a - sinx

for strictly increasing, f'(x) > 0

so, a - sinx > 0 it will be correct for all real value of x only when a ∈ (-1, 1)

Therefore the value of a belongs to (-1, 1)

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Answer 2

Question.

f(x) = ax + cosx is strictly increasing on R.

Answer.

Find the value of (a )=?????

Solution: Here function ,f(x) =a x+cos X

differentiating f(x) with respect to X we get.

f(x)=a+(-sin x)=a -sin x

for strictly ,incresing ,f(x)>0

So a,sun x>0 it will be correct for all real value of x only when a € (-1,1).

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