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Differentiate y=x^2 from first principles

y=x 2 dy/dx= Lim h-->0 ( ((x+h) 2 -x 2 ) / (x+h-x) )dy/dx= Lim h-->0 ( (x 2 + 2hx + h 2 - x 2 ) / h )dy/dx= Lim h-->0 ( (h 2 + 2hx) / h )dy/dx= Lim h-->0 ( h + 2x )dy/dx= Lim h-->0 ( h ) + 2xd...
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Answered by Dipayan C. • Maths tutor
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How to find the turning point on a curve?

The equation of the curve will be a quadratic i.e. it follows the form y=ax 2 +bx+cTo find the turning point, the quadratic will need to be solved using the completing the square method. This means to factor...
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Answered by Muhammad V. • Maths tutor
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Solve 4log₂(2)+log₂(x)=3

First, we should look at the laws of logarithms.log a x+log a y=log a xylog a x-log a y=log a (x/y)klog a x=log a x k We can see that laws 1 and 3 might be helpful, so we simplify our equation.log 2 2 4 +log...
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Prove that the difference between the squares of any two consecutive integers is equal to the sum of these two integers.

A problem of this nature seems complex at first until you break it down and see what it is really asking you to find. We can represent two consecutive integers as x and x + 1. The problem asks us to prove so...
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Simplify 3 × a × 3 × a

The question asks you to simplify an expression, this means we need to write it with as few symbols and numbers as we can.Multiplication is commutative, this means that it doesn't matter which order we do th...
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Answered by Rob G. • Maths tutor
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