Methods 3&4 – Applications of Differentiation (Week 16)
1. For the function 𝑓(𝑥) = 2𝑥 2 − 8𝑥 + 11
(a) Find the average rate of change between 𝑥 = 2 and 𝑥 = 3
(b) Find the instantaneous rate of change at 𝑥 = 2 and at 𝑥 = 3
(c) Why are the values from part a different from part b?
Methods 3&4 – Applications of Differentiation (Week 16)
2. The function 𝑓(𝑥) = 𝑥 2 − 10𝑥 + 28 is shown, as well as the tangent to 𝑓 at 𝑥 = 4.
Find 𝑄 and 𝑆, where the tangent intersects the vertical and horizontal axes.
Q (0,q)
R (4,f(4))
S (s,0)
Methods 3&4 – Applications of Differentiation (Week 16)
3. Find the stationary point(s) of ℎ: [−2, ∞) → ℝ, ℎ(𝑥) = 𝑥 3 + 5𝑥 2 + 7𝑥 + 3 and determine
their nature.
4. Calculate the following
(a)
𝑑
(𝑥 2 )
(sin(𝑒
))
𝑑𝑥
(b)
𝑑
(sin(𝑥) cos(𝑥) tan(𝑥))
𝑑𝑥
Methods 3&4 – Applications of Differentiation (Week 16)
5. For the function 𝑓(𝑥) = 2𝑥 2 − 8𝑥 + 11
(d) Find the average rate of change between 𝑥 = 2 and 𝑥 = 3
(e) Find the instantaneous rate of change at 𝑥 = 2 and at 𝑥 = 3
(f) Why are the values from part a different from part b?
Methods 3&4 – Applications of Differentiation (Week 16)
6. The function 𝑓(𝑥) = 𝑥 2 − 10𝑥 + 28 is shown, as well as the tangent to 𝑓 at 𝑥 = 4.
Find 𝑄 and 𝑆, where the tangent intersects the vertical and horizontal axes.
Q (0,q)
R (4,f(4))
S (s,0)
Methods 3&4 – Applications of Differentiation (Week 16)
7. Find the stationary point(s) of ℎ: [−2, ∞) → ℝ, ℎ(𝑥) = 𝑥 3 + 5𝑥 2 + 7𝑥 + 3 and determine
their nature.
8. Calculate the following
(a)
𝑑
(𝑥 2 )
(sin(𝑒
))
𝑑𝑥
(b)
𝑑
(sin(𝑥) cos(𝑥) tan(𝑥))
𝑑𝑥