Search over 10,000 free study notes

Since L is parallel to y=4x+5 we know that the two lines have the same gradient. The gradient of a line in the form y=ax+b has is a, which means the gradient of y=4x+5 is 4, so L is y=4x+b and we just nee...

A function of the form shown in the question is called a composite function, it is a 'function of a function'. It can be differentiated by expanding the brackets and differentiating each term individually...

Firstly you would start by differentiating the function and equating it to zero as the gradient of the function at the maximum point is zero. to differentiate this function you would use the chain rule si...

Start by differentiating the function to find points where the gradient is 0. so dy/dx = 15x^2 + 18x + 3 We can use the equation for finding the roots of a quadratic here, set a=15, b=18 and c=3 and proc...

We have to use the chain rule here. If we set u to the inside of the bracket, u = x^2 + 3 and differentiating we get du/dx = 2x. Now the original expression becomes y = u^2. Differentiating this with resp...