Mathematics: The quotient of g and 6 is less than 8. find g.

The quotient of g and 6 is less than 8. find g. - id683907400, Lakenwilliams1250

kyrabrown33

11.09.2020

Step-by-step explanation:

Given $g'(x) = g^{-2}, x 0\ g(1) = 0 \ and \ g(2) = 0$

To get g(x), we will have to integrate g'(x)

$g(x) = \int\limits {x^{-2}} \, dx\\ g(x) = \frac{x^{-2+1}}{-2+1} + C\\ g(x) = -x^{-1} + C\\g(x) = -x^{-1} + C\\$

If g(1) = 0, this means at x = 1, g(x) = 0

0 = -1⁻¹ + C

C= 1

Substitute C = 1 into the function

g(x) = -x⁻¹ + 1

If g(2) = 0, this means at x = 2, g(x) = 0

0 = -2⁻¹ + C

C= 2⁻¹

C = 1/2

Substitute C = 2 into the function

g(x) = -x⁻¹ + 1/2

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