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MATH 16A WORKSHEET 12-
(1) The mass of a sample of radioactive material is described by the function f(t), which satisfies the differential equation
F'(t) = (ln 6)f(t)
and satisfies f(1) = 24. Find the formula for f(t). What is f(0)? At what time is f(t) = 144?
(2) Let f and g be two differentiable functions. Find an anti-derivative (in terms of f and g) for each of the following expressions.
(a) f'(x)g(x) + f(x)g'(x)
(b) f'(g(x)) · g'(x)
(c) ef(x)f'(x)
(d) f'(t)/f(t)
(e) 2g(x)g'(x)
(f) x4
(g) (1/x) + x + e3x
(3) Find all functions f(t) such that f'(t) = (-1/x2) + x2 and f(1) = 0.
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