y=(6x^9 +x^8)/(2x^4), work out the value of d^2y/dx^2 when x=0.5

The question can be represented by the notation d2y/dx2|x=0.5, meaning the second derivative of y with respect to x resolved at x=0.5. Since y is in the form f(x)/g(x), the quotient rule could be used, but it would be much easier to first simplify y to 3x5 + x4/2, using the index rules (xm/xn = xm-n). Once y is in this form we can easily differentiate both terms with respect to x twice, giving dy/dx = 15x4 + 2x3, and then d2y/dx2 = 60x3 + 6x2. At this point we can substitute in x=0.5, giving d2y/dx2|x=0.5 = 60(0.5)3 + 6(0.5)2 = 9.

Related Further Mathematics GCSE answers

All answers ▸

A=(1,a;0,1/2) B=(1,-1;0,2) AB=I, calculate the value of a.


How do I determine if a stationary point on a curve is the maximum or minimum?


How can I find the equation of a straight line on a graph?


The curve C is given by the equation x^4 + x^2y + y^2 = 13. Find the value of dy/dx at the point (-1,3). (A-level)


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