Further applications of differentiation 1

The diagram shows a river,500m wide between the straight parallel banks where AD = 500m and   DB = 2000. A man swims across the river from A to C at 0.5 m/s and then he runs along the banks from C to B at 0.8 m/s (a)If he swims in the direction AC making an […]

Equations without stationary points

Given y = 4/√(2x-3), x > 1.5 (a)Find dy/dx (b)Explain why the graph of y = 4/√(2x – 3) does not have a stationary point (c)State whether y = 4√(2x – 3) is an increasing or decreasing function. Explain your answer clearly. y = 4(2x – 3)-1/2 dy/dx = -2(2x – 3)-3/2(2)            = -4(2x […]

Maximum/Minimum gradient of a curve

Find the minimum gradient of the curve y = 2×3 – 9×2 + 5x + 3 and the value of x when the minimum gradient occurs. y = 2×3 – 9×2 + 5x + 3 gradient, m = 6×2 – 18x + 5 dm/dx = 12x – 18 minimum gradient, dm/dx = 0 12x – […]

Maximum point and minimum point 1

A curve with equation in the form of y = ax + b/x  y = ax + b/x2 has a stationary point at (3 , 4), where a and b are constants. Find the value of a and of b. X = 3     y = 4 4 = 3a + b/a —–(1) Y = ax […]

CJC/II/Q4

The diagram shows the region R bounded by the two parabolas        Y = x2 and x = (y – 2)2 – 2  and the y – axis. Find the points indicated A and B in the diagram. (a)Find the area of the region R (b)Find the volume formed when R is rotated 2π radian […]

VJC/2013/Prelim/P1/Q1

(a)Without using a calculator, solve the inequality (b) Deduce the range of values of x that satisfies. Solutions: (a): x≤-6 or 1≤x<3 or x>3                  (b): 0<x≤e-6 or e≤x<e3 or x>e3 (a) (b) lnx ≤ -6               x ≤ e-6   1≤ lnx <3  e≤x<e3  lnx>3  x>e3 […]