can any one find the answer of the following questions with all necessary steps?

Question

1)find the interval of w/h f(x) = 6x-x square in decreasing and increasing
2)Find two positive real numbers with product 81 and sum minimum
3)Find the area of the region bounded by the curve f(x) = x square -1 and g(x) = 7-x square


thank's

Answer 1

For problem (2) we have xy = 81 and d/dx (x + y) = 0

from the first expression y = 81/x substituting into the second we have

d/dx (x + 81/x) = 0 or 1 - 81/x^2 = 0 or 81 = x^2 hence x = + or - 9

since x>0 and y>0 x = 9 and so y = 9

Answer 2

there are 6 billion people in the world so somebody should