(a) what can you say about a solution of the equation y' = - (1/4)y2 just by looking at the differential equation? 1. the function y must be decreasing (or equal to 0) on any interval on which it is defined. 2. the function y must be increasing (or equal to 0) on any interval on which it is defined. (b) verify that all members of the family y = 4/(x + c) are solutions of the equation in part (a). (c) find a solution of the initial-value problem. 3√12x+ 0.008 12

Step-by-step explanation:

a) We can state that the value of y' is negative on an interval because y^2 is positive in any interval (except in y(0), in which y'(0)=0). If y' is negative, as it is the slope of the tangent of the function y in any point, we can conclude that y is decreaing or equal to zero on any interval on which is defined.

b) First, we calculate y'

Then we replace in the differential equation and get the same result

c) The question is not readable, so I am going to solve this initial-value problem:

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4

a

step-by-step explanation:

the denominator cannot be the same as one of the factors.

8 denominator times 2 denominator = 16

and 7 numerator time 11 = 77

77/16= 77/16 ( they cannot be further simplified)