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A curve has equation y=x^2 + 2x +5. Find the coordinates of the point at which the gradient is equal to 1.

dy/dx= 2x+2 , gradient is equal to 1 so dy/dx also equals 1.1=2x+2-1=2xx=-1/2plug this value of x into the equation to get y=17/4
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Answered by Nikhil L. • Maths tutor
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Find the derivative, dy/dx, of y = 8xcos(3x).

Let u= 8x then du/dx = 8Let v= cos(3x) then dv/dx = -3sin(3x)Therefore using the product rule: dy/dx = (cos(3x))(8) + (8x)(-3sin(3x))So dy/dx = 8cos(3x) - 24xsin(3x) .
JC
Answered by Joshua C. • Maths tutor
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what is a standing wave and how is it formed ?

A standing wave is the interference of two sinusoidal waves travelling in opposite directions, confining the wave and its energy to a fixed position, creating nodes and anti nodes . nodes - points where the ...
DN
Answered by Danielle N. • Physics tutor
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How should I structure my personal statement?

It is important to remember that your personal statement should be ' personal '. Therefore, whilst you will need to tick boxes that the admissions tutors are looking for, it should also say something unique ...
JP
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Evaluate the role of technology in prolonging the First World War (IB History Exam Question)

The Examiner is looking for a nuanced but strong answer. Technology's rapid development during WW1 gave rise to the belief that it would cut the war short. However, each technological innovation was quickly ...
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Answered by Tim B. • History tutor
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