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How could I sketch a graph of y=2x^3-3x^2?

To sketch a graph of an equation, there are several key features to consider. Firstly, we can consider where the graph crosses the x- and y-axes. When x=0, y=0, so the graph goes through the origin. If y=0, ...
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Answered by Lawrence H. • Maths tutor
13195 Views

Let f(x)=x^2-ax+a-1 and g(x)=x-5. The graphs of f and g intersect at one distinct point. Find the possible values of a.

If the two graphs intersect, it means that they will share the same y and x coordinates at one particular point. (I will draw diagram to show point). Therefore, you can set f(x)=g(x) so that x^2 -ax +a -1 = ...
AO
Answered by Andres O. • Maths tutor
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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...
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Answered by Ben S. • Maths tutor
4984 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...
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Answered by Benedict R. • Maths tutor
4143 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'...
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Answered by Rania A. • Maths tutor
3793 Views