Prove that the equation y = 3x^4 - 8x^3 - 3 has a turning point at x=2

By definition, turning points occur when the gradient function equals to zero. To prove this we need to differentiate the function given. To differentiate, bring the power down and multiply it by the co-efficient. When we do this we get dy/dx = 12x^3 - 24x^2. Subbing in the value x=2 into this function we get dy/dx = 0. It is important to write a concluding statement with 'prove that' questions. You should write something like ' As the gradient function equals zero at x=2, a turning point must occur here as the gradient is zero' in order to obtain full marks.

Answered by Maths tutor

3563 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

If, f(x) = 8x^3 + 1 / x^3 . Find f''(x).


Show that Sec2A - Tan2A = (CosA-SinA)/(CosA+SinA)


Express 3sin(2x) + 5cos(2x) in the form Rsin(2x+a), R>0 0<a<pi/2


(a) Express 9x+11/(2x+3)(x-1) as partial fractions and (b) find the integral of 9x+11/(2x+3)(x-1) with respect to x


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2026 by IXL Learning