Question

Find the first and second derivatives of the function f(x) = x² - 5x + 8

Answer 1

Answer: Original function is a quadratic

Step-by-step explanation:

To find the first and second derivatives of the function (f(x) = x^2 - 5x + 8), we'll use the power rule for differentiation. The power rule states that if (f(x) = x^n), then (f'(x) = nx^{(n-1)}).

First Derivative (f'(x)):

[f(x) = x^2 - 5x + 8]

[f'(x) = 2x - 5]

So, the first derivative is (f'(x) = 2x - 5).

Second Derivative (f''(x)):

Now, let's find the second derivative by taking the derivative of (f'(x)):

[f'(x) = 2x - 5]

[f''(x) = 2]

So, the second derivative is (f''(x) = 2). The second derivative of the given function is a constant, indicating that the original function is a quadratic.

Answer 2

The first derivative of the function f(x) = x² - 5x + 8 is 2x - 5, and the second derivative is 2.

Step-by-step explanation:

To find the first and second derivatives of the function f(x) = x² - 5x + 8, we apply the basic rules of differentiation. For the first derivative, we differentiate each term separately:

• 
  
• 
  
• 
  

Hence, the first derivative f'(x) is 2x - 5.

For the second derivative, we differentiate the first derivative:

• 
  
• 
  

Therefore, the second derivative f''(x) is 2.