459 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.

10 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

#### 354 SUBJECT SPECIALISTS

£22 /hr

Degree: Mathematics (Bachelors) - Imperial College London University

Subjects offered:Maths

Maths

“21 years old. 2 years experience teaching. BSc Mathematics Imperial College London. Studying MSc in Aerospace Dynamics (please ask for references).”

£26 /hr

Degree: Mathematics (Masters) - Sheffield University

Subjects offered:Maths, Further Mathematics + 3 more

Maths
Further Mathematics
.STEP.
.MAT.
-Personal Statements-

“I am a fun, engaging and qualified tutor. I'd love to help you with whatever you need, giving you the support you need to be the best you can be!”

£30 /hr

Degree: Physics (Masters) - Durham University

Subjects offered:Maths, Physics+ 4 more

Maths
Physics
Music
Further Mathematics
Chemistry
-Personal Statements-

“Hello everyone! My name is Anuradha (you can call me Anu), and I am a Physics Undergrad at Durham. I have always had a “thing” for science and am so pleased to be studying it – and hope that I can give you all the support you need to ...”

£20 /hr

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

Subjects offered:Maths

Maths

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

If we have a vector 4x + 6y + z and another vector 3x +11y + 2z then what is the angle between the two?Give the answer in radians

A line L is parallel to y = 4x+5 and passes through the point (-1,6). Find the equation of the line L in the form y = ax+b.

How do you factorise a quadratic equation?

Find the derivative of the following expression: y=x^3+2x^2+6x+5.

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