Question

The max, value of sin x + cos x is​

Answer 1

Answer:

Step-by-step explanation:

Letf(x)=sinx+cosx⟹f′(x)=cosx−sinx  

For finding the maximum value of f(x) we equate  f′(x)=0  

⟹cosx−sinx=0⟹cosx=sinx⟹x=45∘  

f′′(x)=−sinx−cosx  

f′′(45∘)=−sin45∘−cos45∘=−2–√<0  

Hence x =  45∘  is the maxima

f(x)max=(sinx+cosx)max=sin45∘+cos45∘=2–√≈1.4142