Answer :
Final answer:
The derivative f'(x) of the function f(x) = 5x⁴ - 4x³ + 4x² - 9x + 92 is computed using the power rule, resulting in f'(x) = 20x³ - 12x² + 8x - 9, which is option (a).
Explanation:
To compute the derivative of the function f(x) = 5x⁴ - 4x³ + 4x² - 9x + 92, we apply the power rule of differentiation. The power rule states that if f(x) = xn, then f'(x) = n*xn-1. Using this rule, we differentiate each term of the function separately:
- The derivative of 5x⁴ is 20x³.
- The derivative of -4x³ is -12x².
- The derivative of 4x² is 8x.
- The derivative of -9x is -9.
- The derivative of the constant 92 is 0 because the derivative of a constant is always zero.
Combining these results, we get f'(x) = 20x³ - 12x² + 8x - 9, which corresponds to option (a).
