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.

OC
Answered by Oscar C. Further Mathematics tutor

4377 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

What is the equation of a circle with centre (3,4) and radius 4?


(x+4)((x^2) - kx - 5) is expanded and simplified. The coefficient of the x^2 term twice the coefficient of the x term. Work out the value of k.


f(x) = 3x^3 – x^2 – 20x – 12 (a) Use the factor theorem to show that (3x + 2) is a factor of f(x). [2 marks] (b) Factorise f(x) fully. [3 marks]


write showing all working the following algebraic expression as a single fraction in its simplest form: 4-[(x+3)/ ((x^2 +5x +6)/(x-2))]


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning