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What is differentiation and why is it useful?

Although differentiation is often taught in an abstract way, it's applications are virtually limitless. It's primary purpose is to determine the gradient of a line at a given point on a curve. Unlike with th...
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Answered by Evelyn H. • Maths tutor
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How to draw the inverse of a function ?

There is a simple trick to drawing the inverse of a given function. First, roughly sketch the original function. This means a sketch of the general shape of the curve with some key characteristics such as it...
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Answered by Christina V. • Maths tutor
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What is the tangent line to the curve y = x^3+4x+5 at the point where x = 2?

First, we must find the value of y when x = 2. y = x 3 +4x+5 = (2) 3 +4(2)+5 = 21 Then we must find the gradient of the tangent line. This can be done by differentiating y with respect to x and substituting ...
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Answered by Oliver T. • Maths tutor
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A circle C with centre at the point (2, –1) passes through the point A at (4, –5).....

(a) Find an equation for the circle C. Before tackling a question like this it is always a good idea to draw a rough sketch of all the information that's given to you. The general equation of a circle is x 2...
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Answered by Brodie W. • Maths tutor
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Express 3 cos θ + 4 sin θ in the form R cos(θ – α), where R and α are constants, R > 0 and 0 < α < 90°.

To find the value of R, use Pythagoras's Theorem using the coeffecients of cos θ and sin θ. The correct answer should be R=5. Expand the expression R cos(θ – α). Equate the expanded expression with 3 cos θ +...
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Answered by Anahita G. • Maths tutor
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