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A line L is parallel to y=4x+5 and passes through the point (-1, 6). Find the equation of the line L in the form y=ax+b . Find also the coordinates of its intersections with the axes.

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 need t...
MM
Answered by Matt M. • Maths tutor
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How would I differentiate a function of the form y=(f(x))^n?

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 bu...
MW
Answered by Matthew W. • Maths tutor
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find the coordinate of the maximum value of the function f(x) = 9 – (x – 2)^2

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 since...
SB
Answered by Sruthi B. • Maths tutor
4205 Views

Find the stable points of the following function, determine wether or not they are maxima or minima. y= 5x^3 +9x^2 +3x +2

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 proceed....
YC
Answered by Yusuf C. • Maths tutor
4557 Views

Differentiate y = (x^2 + 3)^2

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 respect...
MH
Answered by Matthew H. • Maths tutor
8425 Views