G(x) = 3 log(x + 7) - 8is this function increasing or decreasing?

Question

`g(x) = 3 log(x + 7) - 8`is this function increasing or decreasing?

Answer 1

Given function : g(x)=3log(x+7) -8

A function is said to be increasing if the derivative of the function is greater than 0,

and it said to be decreasing tof the derivative of the function is less than 0,

Differentiate the given function with respect to x,

[tex]\begin{gathered} g(x)=3\log (x+7)-8 \\ \frac{dg(x)}{dx}=\frac{d(3\log (x+7)-8)}{dx} \\ g^{\prime}(x)=3\frac{d\log (x+7)}{dx}-\frac{d(8)}{dx} \\ g^{\prime}(x)=\frac{3}{x+7}-0 \\ g^{\prime}(x)=\frac{3}{x+7} \\ \text{ since if x}>7\text{ then the function will be negative, } \\ g^{\prime}(x)<0, \\ \text{thus function at }7Answer :

at x >7 , the function g(x) will be decreasing

at x <7 the function g(x) will be increasing.