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How do I calculate where a function is increasing/decreasing?

This depends entirely on the gradient of the function, which is calculated as (dy/dx). At (dy/dx)= 0, the function is neither increasing nor decreasing, since the gradient is zero. The max number of stationa...
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Answered by Steve H. • Maths tutor
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Prove or disprove the following statement: ‘No cube of an integer has 2 as its units digit.’

This is a very standard proof question for the C3 exam. The first thing that I would do when I see wordy proof statements like this is to make sure I understand what it means. Maybe writing out the statement...
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Answered by Thomas D. • Maths tutor
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Solve the simultaneous equations: (1) y – 2x – 4 = 0 , (2) 4x^2 + y^2 + 20x = 0

Rearrange (1): y=2x+4 Subsitute this into (2): 4x 2 +(2x+4) 2 +20x=0 Simplify and collect like terms: 8x 2 +36x+16=0 Factorise: (2x+1)(x+4)=0 Therefore: 2x+1=0 -> x=-0.5 and x+4=0 -> x=-4 Substitute th...
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Answered by Anastasia T. • Maths tutor
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A small stone is projected verically upwards from a point O with a speed of 19.6ms^-1. Modeeling the stone as a particle moving freely under gravity find the time for which the stone is more than 14.6m above O

S = 14.7, U = 19.6, V =, A = -g, T = t using s = ut + 1/2 at^2 14.7 = 19.6t + 1/2 -g t^2 1/2 g t^2 - 19.6t + 14.7 = 0 t = (19.6 +- sqrroot(-19.6 2 - 4 * 0.5 * 9.8 * 14.7)) / 2 * 0.5 * 9.8 t = 1 and t = 3 The...
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Answered by Hamish B. • Maths tutor
5094 Views

Integrate 3x*2 using limits of 3 and 2

(See whiteboard for step by step process) First, we write down the function we want to integrate (3x 2), and include the limits at the top and bottom of our integration sign to show that it's a definite inte...
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Answered by Charlie W. • Maths tutor
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