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Point A lies on the curve: y=x^2+5*x+8. The x-coordinate of A is -4. What is the equation of the normal to the curve at A?

First we will find the gradient of the tangent of the curve at A. So first, we differentiate y with respect to x. We get that dy/dx=2 x+5. We can plug in x=-4 to find the gradient of the tangent at A. We get...
AG
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Find the coordinates of the minimum/maximum of the curve: Y = 8X - 2X^2 - 9, and determine whether it is a maximum or a minimum.

First we need to find the derivative of the curve:dy/dx = 8 - 4X.We can then find the X coordinate by setting this equal to zero: 0 = 8 - 4X, X = 2.Plugging this back into the original equation gives us the ...
ML
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Find the x and y coordinates of the minimum of the following equation: y = x^2 - 14x + 55.

We can see that the quadratic function will be U-shaped, as the quadratic term is with a positive sign. Therefore, the absolute extreme of the function will be a minimum. Step 1: Differentiate to find the sl...
FD
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Can you explain rationalising surds?

Rationalising surds is the process of removing a square root from the bottom of a fraction. The way we do it is by using a little trick involving the difference of two squares.The difference of two squares i...
HA
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A ladder of length 2L and mass m is placed leaning against a wall, making an angle t with the floor. The coefficient of friction between all surfaces is c. At what angle t does the ladder begin to slip?

Firstly draw a free body diagram of the ladder, showing its weight and the contact forces at either end. We'll call end A the top end and end B the bottom end. The next thing to do is to eliminate all the un...
TB
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