Practice — what type is this question? (Differential Calculus)

7.1 Determine f'(x) from first principles if it is given that f(x) = 4 − 7x.

Source: DBE Mathematics Paper 1, November 2019, Question 7.1

7.2 Determine dy/dx if y = 4x⁸ + √(x³)

Source: DBE Mathematics Paper 1, November 2019, Question 7.2

7.4 The curve with equation y = x + 12/x passes through the point A(2 ; b). Determine the equation of the line perpendicular to the tangent to the curve at A.

Source: DBE Mathematics Paper 1, November 2019, Question 7.4

g(x) = x³ + x² − 16x + 20 9.1.2 Determine the coordinates of the turning points of g.

Source: DBE Mathematics Paper 1, November 2018, Question 9.1.2

After flying a short distance, an insect came to rest on a wall. Thereafter the insect started crawling on the wall. The path that the insect crawled can be described by h(t) = (t − 6)(−2t² + 3t − 6), where h is the height (in cm) above the floor and t is the time (in minutes) since the insect started crawling. 8.3 Determine the maximum height that the insect reached above the floor.

Source: DBE Mathematics Paper 1, November 2019, Question 8.3