Given that, dy/dx = 6x^2 - 3x + 4, and y = 14 when x = 2, express y in terms of x.

dy/dx = 6x2 - 3x + 4
To retrieve the original function y from dy/dx you have to integrate the derivative with respect to x.
y = ∫(dy/dx)dxy = ∫(6x2 - 3x + 4)dx
To integrate, the power is raised by one and the whole term is then divided by the new power on x. The constant of integration is to be included since this is indefinite integration.y = 6x3/3 - 3x2/2 + 4x + cy = 2x3 - 3x2/2 + 4x + c
Since values for y and x are given, they can be substituted into the function to solve for c.y = 14 and x = 214 = 2(2)3 - 3(2)2/2 + 4(2) + c14 = 2(8) - 3(4)/2 + 8 + c14 = 16 - 6 + 8 + c14 = 18 + cc = -4Evaluating the function yields a value of c = -4.This value of c = -4 is written back into the function of y to give the final answer:y = 2x3 - 3x2/2 + 4x - 4

CB
Answered by Ciaran B. Maths tutor

5494 Views

See similar Maths Scottish Highers tutors

Related Maths Scottish Highers answers

All answers ▸

Determine for what values of c, f(x)=4x^2-(2c+8)x+4 has no real roots.


How do you solve integrals which are the result of a chain rule e.g. the integral of sin(2x+1)


Solve algebraically the following system of equations: 4x + 5y = -3; 6x - 2y = 5


Work out the angle between the two tangents of the curve y = sin(x) at y = 0 and y = 1


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences