The gradient of a curve is given by dy/dx = 3 - x^2. The curve passes through the point (6,1). Find the equation of the curve.

Since we differentiate a function to find the gradient of a curve at any point, we need to reverse that to find the equation of the curve. We do this by integrating with respect to x:If you have a constant (a number without x), it becomes (constant)x. In this case, 3 becomes 3xThen, if you do have an x, you add one to the power and divide by the new power. So, here, -x^2 will become (-x^3)/3If you're given a point and told to find the equation of the curve, you have to find the constant, c. This is because when you a constant, it becomes zero. To do this, you substitute the coordinates into your integrated form: y = 3x - (x^3)/3 + c. This leads to 1 = 3(6) - (6^3)/3 + c. Solve for c and you'll get 55.So the equation of the curve is y = 3x - (x^3)/3 + 55.Never forget +c!!

DN
Answered by Darya N. Maths tutor

9329 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do you differentiate (3x+cos(x))(2+4sin(3x))?


Particle A mass 0.4kg and B 0.3kg. They move in opposite direction and collide. Before collision, A had speed 6m/s and B had 2m/s. After collision B had 3m/s and moved in opposite direction. Find speed of A after collision with direction and Impulse on B.


(ii) Prove by induction that, for all positive integers n, f(n) = 3^(3n–2) + 2^(3n+1) is divisible by 19


A particle of weight 15N is resting on a plane inclined at an angle of 30°. Find : a) the normal force exerted on the particle, b) the coefficient of friction between the particle and the plane, providing it is in limiting equilibrium


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences