Turn on thread page Beta
    • Thread Starter
    Offline

    12
    ReputationRep:
    8.
    A curve has the equation y=3x^3 - 7x + \frac{2}{x}.
    a,Verify that the curve has a stationary point when x=1
    b, The tangent to the curve at this statsionary point meets y-axis at the point Q. Find the co-ordinates of Q.

    For, a, i have differentiated to get 9x^2 - 2x^-2 - 7.
    After this, i couldnt factorise it like i normally would so i'm not sure how to work out the stationary points?

    b, i have differentiated again for this as well to get the answer as above^^. But i'm not sure what to to after this either?
    • Study Helper
    Online

    15
    Study Helper
    (Original post by Chelsea12345)
    8.
    A curve has the equation y=3x^3 - 7x + \frac{2}{x}.
    a,Verify that the curve has a stationary point when x=1
    b, The tangent to the curve at this statsionary point meets y-axis at the point Q. Find the co-ordinates of Q.

    For, a, i have differentiated to get 9x^2 - 2x^-2 - 7.
    After this, i couldnt factorise it like i normally would so i'm not sure how to work out the stationary points?

    b, i have differentiated again for this as well to get the answer as above^^. But i'm not sure what to to after this either?
    a) Check the question. You're not asked to find the stationary points, only to verify that x=1 gives a stationary point. So, sub x=1 into dy'dx and confirm that it does indeed equal zero.

    b) Since it's a stationary point, the tangent is horizontal, and you just need to work out the y value when x=1. And hence the co-ordinates of Q.
    Offline

    11
    ReputationRep:
    (Original post by Chelsea12345)
    8.
    A curve has the equation y=3x^3 - 7x + \frac{2}{x}.
    a,Verify that the curve has a stationary point when x=1
    b, The tangent to the curve at this statsionary point meets y-axis at the point Q. Find the co-ordinates of Q.

    For, a, i have differentiated to get 9x^2 - 2x^-2 - 7.
    After this, i couldnt factorise it like i normally would so i'm not sure how to work out the stationary points?

    b, i have differentiated again for this as well to get the answer as above^^. But i'm not sure what to to after this either?
    If  x = 1 is a stationary point, then  y'|_{x=1} =0

    b) Note that the gradient is 0 at a stationary point, therefore the tangent at this stationary point will have a gradient of 0. Which means it will be a horizontal line.
    • Thread Starter
    Offline

    12
    ReputationRep:
    (Original post by ghostwalker)
    a) Check the question. You're not asked to find the stationary points, only to verify that x=1 gives a stationary point. So, sub x=1 into dy'dx and confirm that it does indeed equal zero.

    b) Since it's a stationary point, the tangent is horizontal, and you just need to work out the y value when x=1. And hence the co-ordinates of Q.
    Yes,you're right! I didn't read the question properly. Thankyou! For the 2nd part,what equation do i have to put x=1 into? The one that i got when i differentiated or the original one? Because if put x=1 into the differentiated equation, i just get 0 again?
    • Study Helper
    Online

    15
    Study Helper
    (Original post by Chelsea12345)
    Yes,you're right! I didn't read the question properly. Thankyou! For the 2nd part,what equation do i have to put x=1 into? The one that i got when i differentiated or the original one? Because if put x=1 into the differentiated equation, i just get 0 again?
    Since you need the y value when x=1, you'd substitute into your original equation y=....
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: January 9, 2017

2,638

students online now

800,000+

Exam discussions

Find your exam discussion here

Poll
Should predicted grades be removed from the uni application process
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.