Final answer:
The derivative of the polynomial function f(t) = 14t³ - 3t² + 4t - 14 is found using the power rule. The correct derivative is f'(t) = 42t² - 6t + 4, which is option B in the provided options.
Step-by-step explanation:
The student's question involves finding the derivative of the function f(t) = 14t³ - 3t² + 4t - 14. To find the derivative of this polynomial, we apply the power rule, which states that the derivative of t^n with respect to t is n*t^(n-1). Applying this rule to each term in the function:
- The derivative of 14t³ is 42t².
- The derivative of -3t² is -6t.
- The derivative of 4t is 4.
- The derivative of a constant like -14 is 0, since constants do not change as t changes.
Combining these, the derivative of the function f(t) is f'(t) = 42t² - 6t + 4, which corresponds to option B. It is important to note that there seems to be missing '+' signs in the student's original function, as the standard form provided along with the question suggests. Despite the potential typo, we have determined the correct derivative based on standard algebraic principles.