Question

the absolute maximum value of function f(x)=x^2-3x on [0,2]​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The absolute maximum value of the function is 0.

Given:

The function f(x)=x²-3x on [0,2].

To Find:

The absolute maximum value of the function.

Solution:

To solve this question, we will be following the below steps.

Step 1: We will find the first derivative of the given function.

f'(x) = 2x - 3

Step 2: Find the critical point of the function by equating it with 0.

f'(x) = 0 ⇒ 0 = 2x - 3

⇒ x = 3/2.

Step 3: Calculate the value of the function at critical point as well as the end points to find the absolute maximum value.

f(0) =  0 - 0 = 0

f(3/2) = (3/2)² - 3(3/2) = -9/4

f(2) = 2² - 3(2)= 4 - 6 = -2

We observe that maximum value of the function is attainted at x=0 and the absolute maximum value is 0.

∴ The absolute maximum value of the function is 0.

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