MYTUTOR SUBJECT ANSWERS

145 views

What is the equation of the curve that has gradient dy/dx=(4x-5) and passes through the point (3,7)?

To answer this question, we must use our knowledge of integration and differentiation. 

First, we look at the information given to us. We have been told that the gradient of the curve is given by dy/dx=(4x-5). Since the gradient of the curve at a certain point is found by differentiating the equation of the curve, we can find the equation of the curve by integrating the differential. So, to get the equation we have to integrate dy/dx=(4x-5). Integrating this, we get y=2x2-5x+c. 

We are still not finished. This last step is an important step that most people forget! We know that the curve passes through the point (3,7). To find the equation of the curve that satisfies this condition, we have to find the value of the constant c. To do so, we plug in the co-ordinates of the point that lies on the curve where x=3 and y=7. Doing this, we get the equation 7=2(3)2-5(3)+c. Rearranging this equation, we find out that c=7-18+15=4. Therefore, c=4 and the equation of the curve is y=2x2-5x+4. 

Lara B. GCSE Maths tutor, A Level Maths tutor

4 months ago

Answered by Lara, an A Level Maths tutor with MyTutor


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

176 SUBJECT SPECIALISTS

£20 /hr

Dylan P.

Degree: Chemical Engineering (Masters) - Birmingham University

Subjects offered: Maths, Science+ 3 more

Maths
Science
Chemistry
Biology
-Personal Statements-

“I am a third-year student at the University of Birmingham studying my passion, Chemical Engineering. I hope to be able to inspire a similar passion in the sciences and mathematics to help you master the concepts. I am friendly and pat...”

£20 /hr

Nick B.

Degree: Computer Science (Masters) - Bristol University

Subjects offered: Maths, Physics

Maths
Physics

“About me: I am currently studying computer science at the University of Bristol after taking quite a varied set of subjects at A Level. I have always enjoyed helping others when it comes to school. Since I came to university I have bee...”

MyTutor guarantee

£20 /hr

Emily-Louisa S.

Degree: Mathematics (Masters) - Exeter University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“I am in my first year of my mathematics degree at the University of Exeter and one of my favourite things about maths is how it can appear in unexpected situations. For example, in cryptography (the writing and solving of codes of whi...”

About the author

£20 /hr

Lara B.

Degree: MSc Complex Systems Modelling (Masters) - Kings, London University

Subjects offered: Maths

Maths

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Posts by Lara

What is the equation of the curve that has gradient dy/dx=(4x-5) and passes through the point (3,7)?

What is the range of solutions for the inequality 2(3x+1) > 3-4x?

Other A Level Maths questions

How does the product rule for differentiation work

How do you intergrate ln(x)?

Find minimum and maximum of x^2+1 if they exist

How do you solve 3sin2AtanA=2 for 0<A<180?

View A Level Maths tutors

Cookies:

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

mtw:mercury1:status:ok