$1.(20)$ Consider the cost function c$($y$)=$y$2+1.$

a$)(4)$ Derive the average cost function.

b$)(4)$ Derive the marginal cost function.

c$)(4)$ At what level of output is the average cost minimized?

d$)(4)$ Derive the average variable cost function.

e$)(4)$ At what level of output does average variable cost equal marginal cost?