Final answer:
The question lacks specific details to apply the Second Fundamental Theorem of Calculus. To find f'(x), we need the integrand in an integral expression. The theorem states that if f is continuous, the derivative f'(x) is equal to the value of the function being integrated.
Step-by-step explanation:
Unfortunately, the provided question does not contain sufficient information to give a concrete solution to finding f'(x). The Second Fundamental Theorem of Calculus teaches us that if f is continuous on [a, b] and F is an antiderivative of f on [a, b], then:
∫_a^b f(t) dt = F(b) - F(a)
To find f'(x), we need a specific function f(x), which should be the integrand in an integral expression. If we had something like f(x) = ∫_a^x g(t) dt for a continuous function g, the Second Fundamental Theorem of Calculus would tell us that f'(x) = g(x).
Without the explicit function or its integral form, we cannot apply this theorem directly to find the derivative. However, if we consider a position function s(t), its first derivative with respect to time t would give us the velocity v(t), and the second derivative would give us the acceleration a(t).
The complete question is: find f '(x). f(x) = x t 4 5 by using the second fundamental theorem of calculus.