What are the coordinates of the two turning points of the curve y = x^3+3x^2+3?

To find the turning points we need to find dy/dx and set it equal to zero. From there we can find the x coordinate and substitute it back into the origional equation to find the y coordinate.

First we differentiate y = x^3+3x^2+3

We have dy/dx = 3x^(3-1)+23*x^(2-1)+0 = 3x^2+6x

Now we set dy/dx = 3x^2+6x = 0

Both terms have a common factor of 3x so we can take this outside the brackets so the equation looks like dy/dx = 3x(x+2) = 0

From this we can see the equation equals 0 when x takes the values x = 0 and x = -2

We now substitute these values of x back into the origional equation y = x^3+3x^2+3

For x = 0, y = (0)^3+3(0)^2+3 = 3

For x = -2, y = (-2)^3+3(-2)^2+3 = -8+12 +3 = 7

So the coordinates of the two turning points are (-2,7) and (0,3)

LD
Answered by Lauren D. Maths tutor

8121 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve the following quadratic equation: 2x^2 - 5x - 3 = 0


How do you know when to use sin, cos and tan in trigonometry?


There are 892 litres of oil in Mr Aston’s oil tank. He uses 18.7 litres of oil each day. Estimate the number of days it will take him to use all the oil in the tank.


There are 35 people in a group. x(x+1) of them have a blue car, 5x of them have a red car, 4 have a blue and a red car and 4x-8 do not have car. Work out the probability that a person who has a blue car, has a red car as well.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences