# ورقة عمل Rates of Change in Economics and the Sciences الرياضيات المتكاملة الصف الثاني عشر

ورقة عمل Rates of Change in Economics and the Sciences الرياضيات المتكاملة الصف الثاني عشر

Practice of Lesson 9 Rates of Change in Economics and the Sciences

1) Given the cost of manufacturing x items. Find the production level that minimizes the average cost

2) Given the cost of manufacturing x items. Find the production level that minimizes the average cost

3) Let R(x) be the revenue and C(x) be the cost from manufacturing
x items. Find thee maximum profit (in dirhams)
.R(x) = 10x − 0. 001x 2and C(x) = 2x + 5000 (dirhams)

• A) 11000 dirhams
• B) 110000 dirhams
• C) 1100 dirhams
• D) 15000 dirhams

4) The mass of the first x meters of a thin rod is given by the function below. Find the linear mass density at x=1.5, m(x) = (x − 1) 3 + 6x

• A) 6. 75
• B) 9. 125
• C) 6
• D) 2

6) Find the elasticity of demand and find the range of prices for which the
demand is elastic (E ˂ − 1).
f(p) = 200(20 − p)

7) If the concentration of chemical changes according to the given equation. Find the concentration x(t) for which the reaction rate is maximum and find the limiting
x ′ (t) = 0. 5x(t)[5 − x(t)]concentration.

• A) x(t) = 2. 5 the limiting
concentration= 5.
• B) x(t) = 2. 5 the limiting
concentration= 2. 5.
• C) x(t) = 5 the limiting
concentration= 5.
• D) x(t) = 5 the limiting
concentration= 2. 5.

8) The mass of the first x meters of a thin rod is given in the function below. Find the linear mass density function for the rod and describe the composition of the rod.
m(x) = (x − 1) 3 + 6x for 0 ≤ x ≤ 2.

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