Question

Identify intervals on which the function is increasing, decreasing, or constant.

g(x) = 2 - (x - 7)2

Answer 1

differentiate the function
dg/dx = -2x +14
set this equal to zero and solve for x(turns out x=7). this is the point where the slope of the curve is horizontal, i.e constant.
X^2 term is less than 0, so the function looks like this:

So,
x less than 7 is increasing
x greater than 7 is decreasing
x=7 is constant

Answer 2

Thank you

Answer 3

no probs =) you can use differentiation to show which way the curve is oriented too, but unless the question asks for it, it's not really necessary, i prefer to draw the pictures any way