Use calculus to find the absolute maximum value and the absolute minimum value, if any, of the function. (If an answer does not exist, enter DNE.) 5.5

Question

Use calculus to find the absolute maximum value and the absolute minimum value, if any, of the function. (If an answer does not exist, enter DNE.)

f(x) = 9 x − 18 ln(x)    on    [1

2

, 3]

Absolute maximum value: 

 

 at x = 

 

 (Enter your answers as a comma-separated list if there are multiple x-values.)

Absolute minimum value: 

 

 at x = 

 

 (Enter your answers as a comma-separated list if there are multiple x-values.)

Answer 1

Graph the function!

In this case calculus does give the answer.

Differentiate the function and set the derivative equal to zero and solve for x.

The derivative is quite easy to compute!