Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x2 + 7x + 15), [−4, 1]

Question

how to fiind the max ans min

Answer 1

f(x) = ln(x²+7x+15)

 

The absolute extrema occur either at critical points or endpoints.  

 

f'(x) = (2x+7) / (x²+7x+15) = 0 when 2x+7 = 0

 

    The only critical point occurs when x = -3.5

 

To locate the absolute extrema, evaluate f(x) at the critical point and at the endpoints:

 

   f(-3.5) = ln(2.75) = 1.01 ← absolute minimum value

 

   f(-4) = ln3 = 1.0986

 

   f(1) = ln23 = 3.135 ← absolute maximum value