How do I find dy/dx for a given equation, once this is found how do I find the value of x such that dy/dx = 0.

From a given equation y = mx + c. Finding dy/dx allows us to see the gradient of the curve. In order to do this we can follow the formula:When y = xn , dy/dx = nxn-1 . Let us use this in a real scenario. Say we are given the equation y = 3x2 - 6x + 4. We can break this down into stages. First let us differentiate the 3x2. Here the n = 2. So we bring the 2 to the front and subtract 1 from the power: so differentiating 3x2 we have 6x. Now we do the same for -6x. Here the n = 1 so we bring to the 1 to the front and subtract 1 from the power: so differentiating -6x we have -6 (-6x0 = -6). Differentiating a constant results to cancelling that constant so differentiating the 4 results in 0 (as the gradient of a constant function is always 0). Putting all this together we have dy/dx = 6x -6. Now to find the value of x such that dy/dx = 0. We have our dy/dx as shown. We then set dy/dx = 0 and solve the equation. We therefore have 6x - 6 = 0. This implies that 6x = 6. So therefore x =1.

Answered by Sebastian A. Maths tutor

23962 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Using partial fractions find the integral of (15-17x)/((2+x) (1-3x)^2 )


How do I express complicated logs as single logarithms?


Express 6cos(2x) + sin(x) in terms of sin(x), hence solve the equation 6cos(2x) + sin(x) = 0 for 0<x<360


Solve x^2 + x=12 by factorising


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