Hello!

I have tried to solve this question about the functionf(x) = cosx+ sinx

But it was a bit difficult for me.

The question is:

Consider the functionf(x) = cosx+ sinx

a)

(i) Show thatf(– p/4) = 0.

(ii) Find in terms of p, the smallestpositivevalue ofxwhich satisfiesf(x) = 0.

b) The diagram shows the graph ofy= ex(cosx+ sinx), – 2 £x£ 3. The graph has a maximum turning point at C(a,b) and a point of inflexion at D.

(I have attached the diagram)

(i) find dy/dx

(ii) Find theexactvalue ofaand ofb.

(iii) Show that at D,y= sqrt2 e^ p/4

Thank you very much for your help!

Best wishes,

Amine