The curve y = 2x^3 -ax^2 +8x+2 passes through the point B where x = 4. Given that B is a stationary point of the curve, find the value of the constant a.

y=2x3 - ax2 + 8x +2. If we are told that B is the stationary point of the curve, then it is at that point where the gradient of the curve is equal to 0. In order to find the gradient of the curve at this point we must differentiate. Thus we have the equation dy/dx = 6x2 - 2ax + 8. In order to get that equation you must times the integer in front of the x by the numerical value of the power. Then after doing so, you reduce the power by one.
We know that when x=4, the gradient is equal to 0. Therefore, you simply substitute the 4 in the equation and you get 96 - 8a + 8 = 0. Then you want to get your known values on one side and the unknown on the other.Thus you get 104 = 8a104/8 = aa= 13

FM
Answered by Frazer M. Maths tutor

4061 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A ball is fired from a cannon at 20m/s at an angle of 56degrees to the horizontal. Calculate the horizontal distance the ball travels as well as its maximum height reached.


a) Integrate ln(x) + 1/x - x to find the equation for Curve A b) find the x coordinate on Curve A when y = 0.


How do you differentiate (2x+xe^6x)/(9x-(2x^2)-ln(x)) w.r.t. x?


Express 3cos(theta) + 5sin(theta) in the form Rcos(theta - alpha) where R and alpha are constants, R>0 and 0<alpha<90. Give the exact value of R and the value of alpha to 2dp.


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