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Find the x and y coordinates of the turning points of the curve 'y = x^3 - 3x^2 +4'. Identify each turning point as either a maximum or a minimum.

The first part of the problem is solved by differentiating once and equating this to zero: y = x^3 - 3x^2 +4 . dy/dx = 3x^2 - 6x . dy/dx = x(3x - 6) . At the turning points; x(3x - 6) = 0 (turning points occ...
RM
Answered by Robbie M. • Maths tutor
13643 Views

Calculate the derivative of the following function: f(x)=cos(3x))^2

The answer can be found by using the chain rule and simple substitution as well as basic knowledge of differentiation.f’(x)= -6cos(3x)sin(3x)
JM
Answered by Jeff M. • Maths tutor
5163 Views

How should I translate an ablative absolute? I've never managed to get it.

You should always start by translating it with 'with,' so for example, 'with the man having laughed,' 'with the man laughing,' or 'with the man being about to laugh.' If you're not sure of the tense, see wha...
JG
Answered by Joseph G. • Latin tutor
2438 Views

What are the most important trig identities we need to know?

cos^2(A) + sin^2(A) = 1, sin(A+B) = sinAcosB + cosAsinB, cos(A+B) = cosAcosB - sinAsinB, sin2A = 2sinAcosA (if A = B), cos2A = cos^2(A) - sin^2(A) (if A = B), cos2A = 1 - 2sin^2(A) => sin^2(A) = 1/2(1 - c...
BH
Answered by Bowen H. • Maths tutor
4554 Views

Solve the differential equation dy/dx = 6xy^2 given that y=1 when x=2.

This equation can be solved using separation of variables. Firstly we rearrange the equation so that all of the y's are on the left hand side and all of the x's are on the right: 1/y 2 * dy = 6x * dx. Then w...
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Answered by Will S. • Maths tutor
7771 Views