1. Write the derivative of function f, if f(x) is:

(a) (b) (c) (d) (e) (f) 10

(g) (h) (i)

2. Find f'(x) if :

(a) (b)

(c) (d)

(e) (f)

(g) (h)

(i) (j)

3. Find dy/dx of the following functions if :

(a) (b) (c) (d) (e)

(f) (g) (h) (i)

(j) (k)

4. Find the gradient of the tangent at the point indicated:

(a) (b)

(c) (d)

[ans: 12; 14; 2a2; b]

Find the equation of tangent to the folllowing line at the point indicated:

(e) (f)

(g) (h)

[ans: 3x-y-4=0; y=2; x-4y+4=0; 6x-2y-7=0].

5. Find the point on the following curves at which the tangents are parallel to the x-axis:

(a) (b) (c)

[ans: (1/2,-1/4); (3,0); (0,6) and (4,-26)].

6. The curve has a slope equal 4 at the point where x=3, evaluate a.

[ans: a=2].

7. The tangent at the point (1, -3) on the curve cuts the x-axis at P and the y-axis at Q.

(i) Find the equation of the tangent. [ans: x-y-4=0]

(ii) Find the coordinates of P and Q. [ans: P(4,0); Q(0,-4)]

(iii) Find the length PQ. [ans: ]

(iv) Find the value of OP.OQ. [ans: 16]

8. Find the gradient of the normal to the curve at the point (-2, 0), and find where this normal crosses the y-axis. [ans: 1/12; (0; 1/6)].

9. If (where a is a constant and n is positive integer), prove that .

10. Prove that the tangent at the origin to the curve is also a tangent at the point (2,2) on the curve.

11. Find the values of a, b, c if the line passes through (2, 2) and is tangent to y = x at this point and also passes through (0, 2). [ans: a=1/2, b-1, c=2].

12. Find the derivative of

(a) (b) (c) (d) (e)

(f) (g) (h)

13. Find y' for a given value.

(a) (b)

(c) (d)

(e) (f)

[ans: -4; 1; 0; 6; does not exist; -2/27].

14. Given that

(a) find f'(x) (b) sketch y = f(x) and y = f'(x).

(c) what is the value of f'(x) at the min. point y=f(x).

(d) Find the range for which f'(x) > 0.

[ans: 2x-2; 0; x>1]

15. If y = 8 - x3. (a) find dy/dx (b) find x if dy/dx = -12 (c) Find the equation of tangents to the curve y = f(x), if the gradient = -12.

[ans: -3x2; +2; 12x+y-24=0 or 12x+y+8=0]

16. The displacement of a particle is given by

(a) find ds/dt

(b) find the time at which the particle is at rest

(c) find the range of time at which the velocity is negative.

[ans: 30-10t; 3; t>3].