Math problem

Question

Hi,

 

Can somebody help me with this one?

 

Use the derivative to determine the extreme values and the extreme values of the functions of

f (x) = x ^ 2 + 3 / x + 1?

 

Use the derivative to determine the maximum and minimum value of the function f (x) = x + sqrt (1-x²)?

Answer 1

Take the derivative of f(x), set it to zero, and solve for x.  Those x values will be the extreme values:

 

f(x) = x² + 3x^-1 + 1

 

df(x)/dx = 2x - 3x^-2

0 = 2x - 3x^-2

3/x² = 2x

3/2 = x³

(3/2)^1/3 = x

 

You try the second one.  Change the sqrt to a power of 1/2: sqrt(1-x²) = (1-x²)^1/2.  Apply the Chain Rule.