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 curve has equation y = ax^2 + 3x, when x= -1, the gradient of the curve is -5. Work out the value of a.


y = (x+4)(6x-7). By differentiating, find the x coordinate of the maximum of this equation.


Express (7+ √5)/(3+√5) in the form a + b √5, where a and b are integers.


A curve has equation: y = x^3 - 3x^2 + 5. Show that the curve has a minimum point when x = 2.


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