MYTUTOR SUBJECT ANSWERS

417 views

The curve C has equation y = f(x) where f(x) = (4x + 1) / (x - 2) and x>2. Given that P is a point on C such that f'(x) = -1.

Firstly, in order to solve this problem we would need to differentiate f(x) to get f'(x).

To differentiate this we would use the quotient rule. The quotient rule is that:

dy/dx = (V.dU/dx - U.dX/dx) / V^2

where U = the numerator = 4x + 1

and V = the denominator = x - 2

This would give the result of:

dy/dx = ((x - 2)4 - (4x + 1)1) / (x - 2)^2

This would then cancel down to give

dy/dx = -9 / (x - 2)^2

Knowing that dy/dx is equivalent to f'(x), we can eqwuate our expression for dy/dx to the value given in the question for f-(x), which is -1.

-1 = -9 / (x - 2)^2

At this point we can solve for x. Firstly by expanding the bracket.

-1 = -9 / (x^2 - 4x + 4)

From this we can bring the denominator to the top and group all the terms on one side.

-1 (x^2 - 4x + 4) = -9

-x^2 + 4x -4 = -9

x^2 - 4x -5 =0

Now we can solve to find the x coordinates:

(x + 1) (x -5) = 0

giving that x = -1 and x = 5

We can substitute these x values into our equation for f(x) to get the corresponding y values.

There when x = -1

y = f(x) = (4(-1) + 1) / ((-1) - 2)

Giving that y = 1 when x = -1, thus the coordinates are (-1,1)

And when x = 5:

y = f(x) = (4(5) + 1) / ((5) - 2)

so y = 7 when x = 5, thus the coordinates are (5,7)

However, in the question we were given the limit x>2, meaning that the answer cannot be (-1,1) and thus the final answer is (5,7).

Chantelle C. GCSE Maths tutor, 11 Plus Maths tutor, A Level Maths tut...

7 months ago

Answered by Chantelle, who has applied to tutor A Level Maths with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

294 SUBJECT SPECIALISTS

£20 /hr

Georgina R.

Degree: Chemistry (Masters) - Bristol University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Chemistry

“I am a motivated and hard-working student with 3 years of tutoring experience. I am a clear and concise tutor, who believes in a patient approach to learning.”

MyTutor guarantee

£26 /hr

Priya L.

Degree: Economics (Bachelors) - Warwick University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
Economics

“About Me: I recently graduated from the University of Warwick with an Economics degree. I am currently on a gap year before I begin my graduate role as a Management Consultant in October. I decided to tutor because I wanted to spend m...”

£20 /hr

Iebad A.

Degree: Aerospace Engineering (Masters) - Sheffield University

Subjects offered:Maths, Italian

Maths
Italian

“About me: Hello, my name is Iebad and I am an aerospace engineering student at The University of Sheffield. As an engineer, maths is the key to unlock all the solutions to our problems in this field. Since the early years I had a broad...”

About the author

£20 /hr

Chantelle C.

Degree: Civil Engineering (Bachelors) - Southampton University

Subjects offered:Maths, Science+ 3 more

Maths
Science
Physics
Chemistry
Biology

“I am a second year Civil Engineering student at the University of Southampton. From a young age I have loved mathematics and the sciences, the only thing I have loved more is passing on that love to others.  I am a patient and compass...”

MyTutor guarantee

You may also like...

Posts by Chantelle

How can an object be accelerating if it does not change in speed?

The curve C has equation y = f(x) where f(x) = (4x + 1) / (x - 2) and x>2. Given that P is a point on C such that f'(x) = -1.

Why is a diamond harder than graphite if they're made of the same substance?

Other A Level Maths questions

Solve x^2 + 8x +3 = 0 by completing the square.

Differentiate xcos(x) with respect to x

What is the integral of sin^2(x)?

Solve the simultaneous equations y = x + 3, y^2 - x^2 + 3 = -6x

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok