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At x=3, is the polynomial y= (4/3)x^3 -6x^2 + 11 at a maxima or minima?

First, take the first differential: y' = 4x^2 -12x. At x=3 y'= 0 so therefore the function is at a point of inflection. Taking the second derivative: y'' = 8x -12. At x=3 y''= 12. As 12 is greater than 0, th...
JT
Answered by James T. • Maths tutor
4241 Views

Differentiate ((x^2)+1)^2

To differentiate this, we use the power rule and the chain rule. First we differentiate the outside part, which equals 2((x^2)+1). However, because the inside of the square is a function, we have to differen...
AC
Answered by Adrian C. • Maths tutor
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Solve equation 1/x + x^3 + 5x=0

For x!=0, multiply the equation by x to get x^4+5x^2+1=0. Then substitute t=x^2 where t>=0. So the equation has a form t^2+5t+1. Then find the discriminant and two roots. One of the roots t2<0 doesn't ...
JO
Answered by Jakub O. • Maths tutor
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Is a line ax+by+c=0 tangent to a circle?

Get a line a form y=-ax/b-c/b, then substitute into a cirle equation (x-p)^2 +(y-s)^2=r^2. Get a quadratic and find whether a discriminant is equal to zero. If it is then the line is tangent to a circle. Oth...
JO
Answered by Jakub O. • Maths tutor
9735 Views

Why does the second derivative tell us something about a function?

Because by looking at the second derivative of a function you are essentially looking at the rate of change of the rate of change. This carries useful information about a function's behaviour and in some sen...
DJ
Answered by Daniel J. • Maths tutor
4342 Views