A curve has the equation y = (x^2 - 5)e^(x^2). Find the x-coordinates of the stationary points of the curve.

This requires the chain rule and the product rule to be used to differentiate the function. The substitution u = x2 can be used to make this easier. Using this, du/dx = 2x and y = (u-5)eu. Using the product rule, dy/dx = eu + (u-5)eu = eu(u-4). Substituting u = x2 back in, dy/du = (x2-4)ex^2. Now the chain rule can be used to find dy/dx: dy/dx = (dy/du)(du/dx) = 2x(x2-4)ex^2. The stationary points are when dy/dy = 0. ex^2 is always > 0, so either 2x = 0 (x=0) or x2-4 = 0, giving x = -2 and x = 2, so the stationary points are at x = -2, 0 and 2.

OJ
Answered by Oliver J. Maths tutor

3485 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the area between the curves y = x^2 and y = 4x - x^2.


Find the constant term in the expression (x^2-1/x)^9


Describe the set of transformations that will transformthe curve y=x^ to the curve y=x^2 + 4x - 1


How do you find the angle between two vectors?


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