Prove or disprove: (a) h + g has a relative maximum at x0 (b) h-g has a relative maximum at x0.?

Question

Let h and g have relative maxima at x0.

Answer 1

Ryan,

 

You prove both postulates using the derivative (or differential) of a sum (or difference):

 

d(h +/- g)/dx = dh/dx +/- dg/dx

 

Since h and g have a relative maximum at x₀, dh/dx = 0 at x=x₀ and dg/dx = 0 at x = x₀.

 

d(h +/- g)/dx = 0 +/- 0 = 0 at x=x₀ and, thus, h +/- g has a relative maximum at x₀.

 

Michael.