Question

Find the value of this expression. short dash open parentheses short dash 2 close parentheses to the power of 0 space plus space 3 to the power of 1 space plus space open parentheses short dash 4 close parentheses squared space minus space open parentheses short dash 1 close parentheses cubed

Answer 1

Absolute maximum value for this expression is  $( \frac{1}{2} , \frac{5}{4} )$.

What is absolute maximum ?

• The largest value that a mathematical function can have over its entire curve (see curve entry 3 sense 5a) .
• The absolute maximum on the graph occurs at x = d, and the absolute minimum of the graph occurs at x = a.— W.

f(x) = 2x³ - 4x² +2  ,              [ 1/2 , 1 ]

First critical points , by setting f'(x) = 0

   f'(x) = d/dx ( 2x³ - 4x² + 2 )

          = 6x² - 8x

Now 6x² - 8x = 0

        2x( 3x - 4 ) = 0

          2x = 0    or 3x-4 = 0

             x = 0  ,     x = 4/3

Critical points x = 0 , x = 4/3

The critical points are not in the given interval  [1/2, 1 ]

evaluate the function at the end points .

x = 1/2  ⇒    f(1/2) = 2(1/2)³ - 4( 1/2)² + 2

                            = 1/4 - 1 + 2

                            = 1/4 + 1

                            = 5 /4

x = 1 ⇒             f(1) = 2 (1)³ - 4(1)² +2

                             = 2 - 4 + 2  ⇒ 0

∴ absolute maximum = $( \frac{1}{2} , \frac{5}{4} )$

Learn more about absolute maximum

brainly.com/question/13774780

#SPJ4

The complete question is -

Given the function f left parenthesis x right parenthesis equals 2 x cubed minus 4 x squared plus 2; locate the absolute maximum point for this function on the interval open square brackets 1 half comma space 1 close square brackets. a. (1, 0) b. open parentheses 1 half comma space 5 over 4 close parentheses c. only (0, 2) d. open parentheses 2 over 3 comma space 22 over 27 close parentheses.