If f(x)=(x-2)^2, determine the gradient of the tangent to the curve f(x) at x=-2.

Firstly, we will need to determine f'(x) which is the derivative of the function and will give us the gradient at a point. This is easiest done but multiplying out the brackets of f(x) to get the function in trinomial form ax^2+bx=c. This is shown below:f(x)=(x-2)(x-2)f(x)=x^2-2x-2x+4f(x)=x^2-4x+4We then find the derivative using the method detailed below where f(x)=ax^b:f'(x)=(ab)x^(b-1)This gives f'(x)=2x-4To find the gradient at x=-2, we sub in x-2 into f'(x) as the derivative of a function at a point is the gradient of the tangent line at that point.f'(-2)=2(-2)-4f'(-2)=-8Therefore the gradient of the tangent line to the curve at x=-2 is -8.

Answered by Cameron G. Maths tutor

2752 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

2476 adults watch a cricket match. The ratio men : women is 3 : 1 How many more men than women watch the match?


Solve the following, (3/4 + 2/5)^2


In a competition, a prize is won every 2014 seconds. Work out an estimate for the number of prizes won in 24 hours. You must show your working. (4 marks)


Solve the simultaneous equations: 2x-y=x+4; x^2+4y^2=37


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