Q. 94.2( 9 Votes )

What is the maximum value of the function sin x + cos x?

Class 12th NCERT - Mathematics Part-I 6. Application of Derivatives

Answer :

Let f(x) = sin x + cos x,

⇒ f’(x) = cosx - sinx

Now, f’(x) = 0

⇒ cosx - sinx = 0

⇒ cosx = sinx

⇒ tanx = 1

Now,

If f’’(x) will be negative when (sinx + cosx) > 0, means both sinx and cosx are positive.

And, we know that sinx and cosx both are positive in the first quadrant.

Then, f’’(x) will be negative when

f’’(x) = -sinx – cosx = -(sinx + cosx)

Now, let us take x =

Then, by second derivative test,

f will be maximum at x =

And, the maximum value of f is

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