Q. 94.2( 25 Votes )
What is the maxim
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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