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give the coordinates of the stationary points of the curve y = x^4 - 4x^3 + 27 and state with reason if they are minumum, maximum, or points of inflection.

differentiating the equation gives dy/dx = 4x^3 - 12x^2 dy/dx = 4x^2(x - 3)

at a turning point, dy/dx = 0. Solving the equation 4x^2(x - 3) = 0 yeilds x = 0, x = 3

putting 0 and 3 back into ...

Answered by Matthew B. • Maths tutor

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If 0<x<1, find the following sum: S = 1+2x + 3x^2 + 4*x^3 + ...

The first thought when trying to solve such a problem is that you might be able to write this sum as a geometric progression. Luckily, it is the case here as well, as we can observe that S is the derivati...

Answered by Horia M. • Further Mathematics tutor

2792 Views

How far do you think Augustus’ building programme in the city of Rome was motivated by practical considerations and how far by other factors?

Augustus needed to solidify his power following the politically chaotic civil wars which culminated in the Battle of Actium in 31BC. A building program was required due to funds most likely being diverted...

Answered by Emma F. • Classical Civilisation tutor

7298 Views

Evaluate the impact of a price ceiling

A price ceiling is defined as a maximum price for a good set below the market equilibrium price, typically to protect the consumers of that specific good. Rent controls in the housing market are an exampl...

Answered by Ludovic A. • Economics tutor

14135 Views