Identify the relative maximum value of g(x) for the function shown below g(x)=7/x^2+5

Answer 1

g(x) = 7/(x²+5) (I'm assuming this is what was meant)

g'(x) = -14x/(x²+5)²

Setting g'(x) to 0 and solving for x, x = 0

g(0) = 7/5 = 1.4

Using 2nd derivative test

g''(x) = 14(3x-5)/(x²+5)³

g''(0) = -0.56 <0 so g(0) = 1/4 is a maximum