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
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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
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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).
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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
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