# What are the global and local extrema of #f(x)=4x-x^2 # ?

##### 1 Answer

Feb 12, 2016

#### Answer:

#### Explanation:

Assume that the domain of

Complete the square

#f(x) = -(x-2)^2-4#

As anything squared cannot be less than zero,

To show using calculus, take the first derivative of

#f'(x) = 4-2x#

Solve for

#4-2x=0#

#x=2#

Perform the second derivative test.

#f''(x) = -2#

#f''(2) = -2 < 0#

This means that the gradient is decreasing at

This means that the gradient changes from positive to zero to negative in a small neighborhood around

This means that

There are no other local extrenum and