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How can I find the normal to a curve at a given point?

Take the curve y = 2x² - 4 and point P (2,4). a) First, find the straight line tangent to the curve at point P

Answered by Artyom P. • Maths tutor

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Sketch y = 9x – 4x^3, showing where the curve crosses the x axis.
First you should look at the equation and try and get a sense of the general shape of the graph. The highest power in here is a 3, so this is a cubic graph. The coefficient (number in front of the x^3) is...
Answered by Anais E. • Maths tutor
4429 Views

Solve (x^2 - 4)/(2x+4)
The common mistake the students make is to simplify the fraction before factorising numerator and denominator. Here, we need to see that the numerator: x^2 - 4 is a difference between squares
Answered by Martina M. • Maths tutor
3069 Views
In year 11, 3/7 of pupils go on holiday abroad in the summer break. Out of these, 1/3 go to France. Determine the ratio of pupils who go to France in summer to pupils who do not go to France in summer.
We can approach this question by breaking it into two steps; first use the information given to work out what proportion of pupils in year 11 went to France. Once we have this, we can go on to find the ra...
Answered by Anisah S. • Maths tutor
2296 Views
How do you find the x co-ordinates of the stationary points of a curve with the equation y = 10x - 2x^2 - 2x^3
First to find the stationary points, you have to differentiate the equation of the curve y, to give you (dy/dx) = 10 - 4x - 6x^2After differentiating the equations, the points at which the curve is statio...
Answered by David M. • Maths tutor
2840 Views
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How can I find the normal to a curve at a given point?

Sketch y = 9x – 4x^3, showing where the curve crosses the x axis.

Solve (x^2 - 4)/(2x+4)

In year 11, 3/7 of pupils go on holiday abroad in the summer break. Out of these, 1/3 go to France. Determine the ratio of pupils who go to France in summer to pupils who do not go to France in summer.

How do you find the x co-ordinates of the stationary points of a curve with the equation y = 10x - 2x^2 - 2x^3

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