𝑥→3lim𝑥

2 −𝑥−

𝑥−

Question 5 Determine from first principles. 𝑦 = 3𝑥 2 − 6 Question 6 Determine the gradient of the tangent to the following curve at the point x = 3. 𝑦 = 𝑥 2 − 𝑥 − 6 Question 7 Differentiate the following with respect to x.

a. 𝑦 = − 7 𝑥− 4√𝑥+ 𝑒 2

b. 𝑦 =(4 −√𝑥) 2 c. 𝑦 = 3𝑥 2 +𝑥 12 2 − 2𝑐 Question 8 Sketch the following curves. Include the turning points (with the help of differentiation), as well as the x and y intercepts. a. 𝑦 = 𝑥 3 − 6𝑥 2 + 8𝑥 b. 𝑦 = −𝑥 3 − 2𝑥 2 Question 9 a. Find the roots of 𝑦 = −𝑥 3 + 9𝑥 b. Determine the turning points of 𝑦 = 𝑥 3 − 𝑥 2 − 𝑥 Question 10

Determine 𝑑𝑦𝑑𝑥 by using rules of differentiation.

a. 𝑦 = 4 𝑥+ 6√𝑥

b. 𝑦 = 14 𝑥 4 +2𝑥 12

Question 11 Determine the x coordinates of the turning points of the graph represented by: 𝑦 = 𝑥 3 − 6𝑥 2 + 9𝑥

ACTIVITIES

Differential Calculus

Question 1

Determine the gradient of the tangent to the following curve at the point x = 3.

𝑓(𝑥)= −𝑥(𝑥 + 2)

Question 2

Determine the gradient of the curve 𝑦 = 𝑥2+ 4𝑥 − 8 at the point x = - 8

Question 3

Given the equation:

𝑦 = 3𝑥2

a. Differentiate rom first principles.

b. Determine the gradient at the point when x = 3.

Question 4

Determine

lim

𝑥→3

𝑥2−𝑥−6

𝑥−3

Question 5

Determine from first principles.

𝑦 = 3𝑥2− 6

Question 6

Determine the gradient of the tangent to the following curve at the point x = 3.

𝑦 = 𝑥2− 𝑥 − 6

Question 7

Differentiate the following with respect to x.

Differential Calculus DAM ACT

Business Mathematics

Damelin

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ACTIVITIES