Final answer:
The derivative of the function f(t) = 4t - 9t² is 4 - 18t.
Step-by-step explanation:
The derivative of the function f(t) = 4t - 9t² can be found using the definition of derivative. The derivative measures the rate at which the function is changing at a specific point. To find the derivative of this function, we need to find the limit of the difference quotient as h approaches 0:
f'(t) = lim(h→0) [f(t + h) - f(t)] / h
Substituting the given function:
f'(t) = lim(h→0) [(4(t + h) - 9(t + h)²) - (4t - 9t²)] / h
Next, we simplify the expression and evaluate the limit to find the derivative:
f'(t) = 4 - 18t