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x^2 - 10x + 21 = 0

First, factorise the quadratic equation. Find two numbers that multiply to give 21 and add to give 10. 7 and 3 (x-7)(x-3)=0 Now find the value x so that when these brackets are multiplied together the answer...
BS
Answered by Ben S. • Maths tutor
5063 Views

Find the derivative of f(x)=x^2*e^x+x

You can split the derivative into 2 parts: dx/dy (x^2*e^x) + dx/dy (x) For the first part you have to use the product rule, so let U=x^2 V=e^x U'=2x V'=Chain rule V'=dx/dy(e^x) dx/dy(x)=e^x 1=e^x Returning t...
BR
Answered by Benedict R. • Maths tutor
4222 Views

We have the curve f(x) = (x^2-5x)(x-1)+ 3x. Sketch the graph y=f(x), making sure to plot the co-ordinates where the curve meets the axes.

The first thing we want to do is re-write the curve f(x) in a format in which we can read and easily plot a graph. If we can include the '3x' in the factorised part of the equation, it will be neater and we'...
RA
Answered by Rania A. • Maths tutor
3861 Views

Find the gradient of y=6x^3+2x^2 at (1,1)

In order to find the gradient of the curve at (1,1), we must first differentiate the equation of the curve. To do this, multiply the coefficient of x by the power of that same x. Then subtract one from the p...
BB
Answered by Ben B. • Maths tutor
5778 Views

A is the point with coordinates (1, 3) B is the point with coordinates (–2, –1) The line L has equation 3y = 4 – 2x Is line L parallel to AB?

No it is not parallel, here is the reasoning. First we work out the gradient of the line AB. We do this by using the gradient formula (Y2-Y1)/(X2-X1). Our points are A=(1,3) rewritten as (X1,Y1) and B=(-2,-1...
EL
Answered by Emily L. • Maths tutor
13900 Views