Top answers

A stationary point of inflection implies a second derivative of 0, does this work the other way around?

No, and we may take a counterexample to see why. If y=x^5+5/3x^4, dy/dx=5x^4+20/3x^3, d2y/dx2=20x^3+20x*2=20x^2(x+1). Setting this to 0 will give us the candidates for a POI, but not all these numbers will b...
TR
Answered by Toby R. • Maths tutor
4168 Views

Integrate x*(5e^x)

Using integration by parts let U=x therefore du=dx.Let dv=5e^x therefore v=5e^x.answer = x*5e^x - integral(5e^x) = (x-1)(5e^x)
MS
Answered by Maximillian S. • Maths tutor
4673 Views

Differentiate y=(5x^4)cos(2x)

Using chain and product rule.dy/dx=(20x^3)cos(2x) - (10x^4)sin(2x)
MS
Answered by Maximillian S. • Maths tutor
4940 Views

A matrix M has eigenvectors (3,1,0) (2,8,2) (1,1,6) with corresponding eigenvalues 1, 6, 2 respectively. Write an invertible matrix P and diagonal matrix D such that M=PD(P^-1), hence calculate M^5.

Without even knowing M, the candidate can calculate M^5. This will follow from the fact that P is the matrix consisting of the eigenvectors of M as columns, and D will have the eigenvalues (in matching colum...
CB
Answered by Cameron B. • Maths tutor
3706 Views

A smooth 4g marble is held at rest on a smooth plane which is fixed at 30 degrees to a horizontal table. The marble is released from rest - what speed is the marble travelling at 5 seconds after being released? Let g = 9.8ms^2

This question involves forces and kinematics. First begin by drawing the situation and identifying the forces acting on the marble. The weight of the marble acts vertically downwards and is equal to the mass...
MR
Answered by Maya R. • Maths tutor
3688 Views