Final answer:
The second derivative of the function f(x) = 4x² - 3x + 26 is a constant value of 8, which is obtained by differentiating the function twice.
Step-by-step explanation:
Finding the Second Derivative
To find the second derivative of the function f(x) = 4x² - 3x + 26, we first find the first derivative f'(x) and then differentiate it again to find the second derivative f''(x). Using the definition of the derivative, the first derivative f'(x) of the function is calculated as:
f'(x) = d/dx(4x²) - d/dx(3x) + d/dx(26)
f'(x) = 8x - 3
Now, we take the derivative of f'(x) to find f''(x):
f''(x) = d/dx(8x - 3)
f''(x) = 8
The second derivative of the function f(x) is just the constant 8, indicating that the acceleration (in the context of motion) is constant, and the function represents the motion of an object in a linearly increasing velocity.