I would like to know how to test concavity or convexity of the following functions below

3. For the Cobb - Douglas production function f(x,, x, ) = Ax" x? , with A > 0, a, B > 0defined on R. , show that Euler's Theorem applies. 4. Show that the following functions are homothetic but not homogeneous. (i) f (x ,x2 ) = k+ xxx for k = 0a constant. (ii) f( x, ,x2) =et 5. Illustrate Euler's Theorem for the Cobb - Douglas production function defined on R. , and Sa, =1. 6. Consider the following specific CES production function defined on R. : y= f(x,,x2)=[0.3x, 2 +0.7x,2] (i) Show that fis concave. (ii) Show that fis homogeneous, and find its degree of homogeneity. (iii) Is the function 0.3x, ? +0.7x,+1 homothetic? (iv) Show that Euler's Theorem applies