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

6286 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do I integrate ln(x), using integration by parts?


The circle (x-3)^2 +(x-2)^2 = 20 has centre C. Write down the radius of the circle and the coordinates of C.


Find the gradient of the tangent and the normal to the curve f(x)= 4x^3 - 7x - 10 at the point (2, 8)


give the coordinates of the stationary points of the curve y = x^4 - 4x^3 + 27 and state with reason if they are minumum, maximum, or points of inflection.


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences