Let Curve C be f(x)=(1/3)(x^2)+8 and line L be y=3x+k where k is a positive constant. Given that L is tangent to C, find the value of k. (6 marks approx)

SO when we see the word tangent we should be thinking about rate of change. Recall that the line being a tangent means they meet and have the same derivative at this point OR we find k such that f(x)-y=0 has a double root. (We can prove that this is true!)So(1/3)x^2+8-k-3x=0 so we solve for k such that the discriminant is 0. that is 9-4(1/3)(8-k)=0 This implies k=8-27/4=5/4

Related Further Mathematics GCSE answers

All answers ▸

How do I know I can multiply two matrices and if so, how do I do it?


How do you use derivatives to categorise stationary points?


The line y = 3x-4 intersects the curve y = x^2 - a, where a is an unknown constant number. Find all possible values of a.


Find the stationary point of 3x^2+7x


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