Question

Over what interval is the graph of f(x) = –(x + 8)2 – 1 decreasiang help

Answer 1

Please use " ^ " to denote exponentiation:  

f(x) = –(x + 8)^2 – 1 
Find the first derivative:  f '(x) = -2(x+8)(1)
Set this = to 0:  -2(x+8) = 0
solve for x:  x = -8
Divide the number line into subintervals based upon x=-8:

(-inf, -8) and (-8, inf)

Choose a test value for x from each interval, e. g., -10 from the first interval and 20 from the second.

Subst. this test value into the derivative, shown above.

If the result is + the function is incr on that interval; if - the fn. is decr.

Questions welcome!