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Why does differentiation give us the results that it does?

A quick analysis here is based on the fact that y=(x 2 ). A big change is worked out between two points. The gradient between x=1 and x=2 is equal to 3. BUT we know the gradient is constantly changing so thi...
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Answered by Alexander A. • Maths tutor
4194 Views

If I have a picture of a graph f(x), how can I draw what |f(x)| and 3f(x-2) look like?

This is about a topic called graph transformations. It can get quite complicated, but the lucky thing here is that each question can be broken down into steps. So considering the first question with |f(x)|, ...
JH
Answered by Jamie H. • Maths tutor
9277 Views

How was the quadratic formula obtained.

We want a solution to ax^2+bx+c=0. Complete the square to get a[(x+b/2a)^2 -(b^2)/(4a^2)]+c=0. Expalding brackets and rearanging gets a(x+b/2a)^2=(b^2)/4a -c. Divide by a to get (x+b/2a)^2= b^2/4a^2 -c/a=(b^...
JH
Answered by Jon H. • Maths tutor
4020 Views

A particle P moves with acceleration (-3i + 12j) m/s^2. Initially the velocity of P is 4i m/s. (a) Find the velocity of P at time t seconds. (b) Find the speed of P when t = 0.5

Solution: V = V (0) + a *t From the question: a = (-3 i + 12 j ); V (0) = 4 i V at time t seconds: V = 4 i + (-3 i +12 j )*t V = 4 i + (-3t i + 12t j ) V = 4 i – 3t i + 12 t j m/s *Bold letters are vectors A...
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Answered by Artur R. • Maths tutor
7227 Views

How do you differentiate a function?

The differential of a function is defined by the expression: dy/dx = Lim(dx->0) of (f(x+dx)-f(x))/dx. For functions only involving powers of x, the differentioal can easily be calculated by timesing by th...
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Answered by Max H. • Maths tutor
4109 Views