Math problem derivation

Question

Hi,

 

I need urgent help to solve these problems:

 

1. What are the fuctions f(x)= x²+3 / x+1  extreme values?

 

2. Define with derivation fuction f(x)= x+sqrt(1-x²) biggest and smallest value.

 

Answer 1

1) Graph the function.

    The derivative is [2x(x +1) - (x² + 3)]/(x + 1)² = (x - 1)(x + 3)/(x + 1)² which has roots at -3 and 1.

     x = 1 is a relative minimum and x = -3 is a relative maximum

     The function blows up at x = -1 and is unbounded positively for large x and negatively as x goes to -∞ which means             there are no absolute maxima or minima.

 

2} Graph the function.  It has real values only on the closed interval [-1,1].

     The absolute minimum occurs at x = -1

     The absolute maximum occurs at x = (1/2)√2

     The derivative is 1 - (x/sqrt(1 - x²)