If f(x)=(4x^2)-(8x)+3, find the gradient of y=f(x) at the point (0.5,0)

When you see the question asking you to find the gradient at a point in the curve, the first thing you have to do is differentiate. This is because when we differentiate, we find the equation of the tangent to the curve at that point, which is the same as the gradient. So for this equation, we can differentiate by using the main differentiation rule which is when y=xn, dy/dx=nxn-1. Using this we will get: dy/dx= f'(x) =(4x2)x(2-1)-(8x1)x(1-1)+(3x0)x(0-1) = 8x-8We then substitute in the point (0.5,0) where x=0.5 to get: f'(0.5)=-4The gradient at the point (0.5,0) is equal to -4.

GK
Answered by Girthanaah K. Maths tutor

6099 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the equation of the tangent to the curve y = (2x -3)^3 at the point (1, - 1), giving your answer in the form y = mx + c.


Given that cos(x) = 1/4, what is cos(2x)?


Use integration by parts to find ∫ (x^2)sin(x) dx. (A good example of having to use the by parts formula twice.)


Find dy/dx, given that y=(3x+1)/(2x+1)


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