Content
Access custom-built, exam-style problems for differentiation. Each problem has a full solution and mark-scheme, as well as AI grading and support.
Select a Difficulty:
11 / 34 problems visible - Upgrade to view all problems
!!
0 / 8
Patrick has a 5cm×8cm rectangular piece of cardboard. He is making an open-top box by cutting equal squares of side length h from each corner of the sheet, and then folding up the sides.
Powered by Desmos
Find an expression for the volume of the box V(h).
Find an expression for V′(h).
Hence, find the value of h that maximizes V
!
0 / 9
Consider two curves defined by
Find f′(x) and g′(x).
Solve f′(x)=g′(x).
State the values of x at which the two curves touch.
Find the equation of their common tangent line in the form y=mx+c.
!
0 / 9
!
0 / 9
!
0 / 9
!
0 / 9
!
0 / 5
!
0 / 5
!
0 / 7
Ask Plex AI about problem 16
Get hints, ask questions, and work through this problem step by step