Q4: You need to review the **geometrical applications of differentiation** topic.

f(2) = 8 implies that at x = 2, the function value f(x) is 8, i.e. (2,8)

f'(2) = 6 > 0 implies the function is increasing at x = 2, i.e. sloping upwards

f''(2) = 2 > 0 implies the function is concave up at x = 2, i.e. direction of bending is upwards.

Hence, A is the correct answer.

FYI: This is 2U, not extension 1.

Q7: Think of a way to connect HK with the given information, this case what's common is HJ. You can find HJ by applying the sine rule, where the missing angles, HJI = 180 - 74 = 106 (adj supp angles add up to 180) and JHI = 180 - 106 - 30 = 44 (angle sum of a triangle is 180), or you can find JHI using the exterior angle is equal to the opposite interior angles property.

Apply the sine rule for triangle HJI, HJ/sin30 = 16/sin44 => HJ = 16sin30/sin44.

Finally, apply trig for right angled triangles for HKJ, sin74 = HK/HJ => HK = 11.07cm

Q9: Refer to finding volumes using integration and review what you can use even functions, B is the correct answer