Question

A. Find y in terms of x if ????y????x=x6y−7 and y(0)=4. y(x)= (8/7x^7+4^8)^(1/8) . B. For what x-interval is the solution defined? (Your answers should be numbers or plus or minus infinity. For plus infinity enter "PINF"; for minus infinity enter "MINF".) The solution is defined on the interval: `

Answer 1

Explanation:

part A)

given

`x=x6y-7`

so y in terms of x would be

`y=(x+7)/x6`

part b)

in order to find intervals of function, we determine the intervals where the function has a positive first derivative . To find intervals, first we find the critical values, or points at which the first derivative of the function is equal to zero. For the given function the intervals would be

put zero in equation

`y=(x+7)/6x`

`y= infinity`

put 1

`y=1.333`

put 2

`y= 0.75`

put 3

`y= 0.555`

hence we can see that the interval is from zero to positive infinity

(PINF)