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Show that the curve y =f(x) has exactly two turning points, where f(x)= x^3 - 3x^2 - 24x - 28

This question is about turning points of a curve, these occur when the gradient of a line is zero. In its current form, the equation of the curve tells us nothing about the gradient of the curve; it must be ...
JA
Answered by Joshua A. • Maths tutor
5852 Views

How would you differentiate and integrate 2x^3?

Integration is the opposite of differentiation.First of all take your 2x 3 So in differentiation you would times the power by the coefficient and then minus one from the power.This would give,6x 2 in other w...
SK
Answered by Scarlett K. • Maths tutor
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How do you use the chain rule?

The chain rule is used to differentiate when there is a function within another function. For example y=(4x+6) 0.5 , y=(x+1) 3 The general formula for the chain rule is dy/dx= dy/du * du/dxAn example of this...
FC
Answered by Frances C. • Maths tutor
4140 Views

Find the turning value of the following function, stating whether the value is min or max, y = x^2 -6x + 5

First the student needs to differentiate the function to find dy/dx = 2x-6At dy/dx = 0, we know the curve is stationary. Now we can work out the x value such that x = 3Put x=3 back into the original equation...
JW
Answered by Joseph W. • Maths tutor
5094 Views

solve 3 cos (2y )- 5 cos( y)+ 2 =0 where 0<y<360 degrees

cos(2y)= (cos(y))^2 - (sin(y))^2 identitynow consider identity (cos(y))^2+(sin(y))^2=1by rearranging this to (cos(y))^2 - 1 = - (sin(y))^2 we can now substitute it into our first identity to obtaincos(2y)= 2...
LS
Answered by Leah S. • Maths tutor
4143 Views