Evil combination: Chem and Calc & Finding a Function

Hi there,

Two questions that have done my head in for the past couple of days; mind taking a look?

**Question one**

For the function *y* = *c*(*e^-at – e^-bt*)

With *a, b, c, > 0 *and *t *≥ 0, find

i)* y *(0)

ii)the limit of *y* as *t* approaches infinity

iii)the point at which *y* reaches a maximum

**Question two**

In water and in solution the product of the concentrations of hydronium ions, [H3O+] and of hydroxyl ions, [OH-] is very close to 10^-14 (in moles).

Let S = [H3O+] + [OH-]

Determine the value of [H3O+] which minimises S.