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The equation x^3 - 3*x + 1 = 0 has three real roots; Show that one of the roots lies between −2 and −1

In order to prove that one real root of an equation is situated in a certain interval, we calculate the value of the function at the ends of the given interval. In the given case, f(-2) = (-2)^3 - 3*(-2) ...

Answered by Paul T. • Maths tutor

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y=4x^3+6x+3 so find dy/dx and d^2y/dx^2

dy/dx=12x^2+6 d^2y/dx^2=24x

Answered by Swapnil P. • Maths tutor

4821 Views

The straight line L1 passes through the points (–1, 3) and (11, 12). Find an equation for L1 in the form ax + by + c = 0, where a, b and c are integers

When finding the equation of a straight line there are two important figures to calculate. The first being the gradient (the slope of the line) and the second being the y intercept (where the line crosses...

Answered by Ruby B. • Maths tutor

19001 Views

Use Simpson's rule with 5 ordinates (4 strips) to find an approximation to "integral between 1 and 3 of" 1/sqrt(1+x^3) dx giving your answer to three significant figures.

Just as a note before I start, some of the symbols I use here will be horribly confused, this won't be an issue with a whiteboard but doing maths in a text editor is not great so I've had to make do.

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Answered by Dominic A. • Maths tutor

9255 Views

Find the turning points and their nature of the graph y = x^3/3 - 7x^2/2 + 12x + 4

Answer = (3,17.5) maximum (4,17.33) minimum

First differentiate y = x^3/3 - 7x^2/2 + 12x + 4 to find dy/dx. Now, at turning points dy/dx = 0 and factorise to find x when dy/dx = 0. Put x back into ...

Answered by John S. • Maths tutor

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