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Topic 3: Differential Calculus FOCUS QUESTIONS 3.2:2 1. Find the derivative from first principles of: a. f(x) = x – 2 b. g(x) = x 2 + 1 c. j(x) = x 3 1 d. k(x) = x + 2 e. l(x) = 1 √x f. m(x) = x 2 – 2x 2. Find from first principles a. f '(2) if f(x) = x 2 + 3x 1 b. g'(– 1) if g(x) = 2x c. y'(3) if y(x) = 5 – 2x 2 2 d. F'(– 2) if F(x) = x+3 3. Find from first principles a. A'(r) where A(r) = πr 2 b. s'(t) if s(t) = 6t 2 + 5t – 2 4. The displacement of an object is given by s(t) = t 2 – 4t m/sec. Using first principles, find the velocity function v(t) = s'(t). 1 5. The velocity of an object is given by v(t) = 2t – 1 m/sec for t ≥ 1. Using first principles, find the acceleration function a(t) = v'(t). – 6. The quantity of pollution in the atmosphere at time t (years) is given by q(t) = 2√ t, t ≥ 1. Using first principles, find the rate at which the pollution changes at time t years. Essentials Text Book 129