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. 

Samradnyee K. GCSE Maths tutor, A Level Maths tutor, GCSE Further Mat...

3 months ago

Answered by Samradnyee, an A Level Maths tutor with MyTutor

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


£24 /hr

Emma M.

Degree: Natural Sciences (Bachelors) - Durham University

Subjects offered: Maths, Psychology


“ I am currently studying Natural Sciences (Maths and Psychology) at Durham University. I have had a passion for Maths and Psychology since the moment I started studying them and am keen toshare my enthusiasm for these subject through ...”

£20 /hr

Tiarnan B.

Degree: MChem (Masters) - York University

Subjects offered: Maths, Geography+ 2 more

-Personal Statements-

“About Me: I am a student of Chemistry at the University of York studying for a masters degree and am a self-confessed science nerd! My goal is to give you the help you need, build your confidence and push you to be the best you can. A...”

£22 /hr

Abi R.

Degree: Engineering (Bachelors) - Exeter University

Subjects offered: Maths, Physics+ 3 more

Design & Technology
-Personal Statements-

“About me: I'm in my first year at the University of Exeter studying Mechanical Engineering. My favourite subjects are Maths & Science and my physics teacher is who inspired me to really love teaching others. He was great at using ana...”

About the author

£20 /hr

Samradnyee K.

Degree: Biomedical Engineering (Bachelors) - Kings, London University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“Hi, I am a Biomedical Engineering student at King’s College London. Mathematics and Physics have always been my passion and I hope to pass on my love for the subjects to you through engaging and interactive sessions specially catered ...”

MyTutor guarantee

You may also like...

Posts by Samradnyee

The variable x=t^2 and the variable y=2t. What is dy/dx in terms of t?

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?

What is the simplest form of the fraction (8a^2+10ab)/(12a+15b)?

Other A Level Maths questions

How do I differentiate sin^2(x)?

Statistics: Dave throws a ball at a bucket. The probability the ball goes into the bucket is 0.4. Dave throws the ball four times. What is the probability that he gets it in twice?

How do I integrate terms with sin^2(x) and cos^2(x) in them? For example integrate (1+sin(x))^2 with respect to x

How do you derive the quadratic formula?

View A Level Maths tutors


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