Practice SAC - Functions and Calculus Help.

[ch]

I need some help with this practise SAC question could someone please help.

Two functions represent a skate ramp with the equations 1/8 (x-4)^2+1 for [0,4] and 0.15(x-4)^3+1 for [4,7] All distances are given in metres.
A) Explain using calculus one there is a smooth transition between the two parts of the ramp.
B) Why given real life situations are 3 decimal places a suitable accuracy?

[Zealous]

For part A, you need to show that the tangent at (the point where the function changes) is the same as x approaches 4 from the left and as it approaches 4 from the right.

So derive the first equation, and sub in . Then derive the second equation and sub in . The result should be the same, thus a smooth transition between functions.

Spoiler

1st Function:


2nd Function:


Sub in x=4 into both.

1st Function:


2nd Function:


Both equal 0.

edits:fixing my fail latex.

For B I don't know for sure why 3 decimal places is a suitable amount of accuracy, but I can assume that it is because in life we measure continuous values (as opposed to discrete), for example our height could be 1.7645321... metres, so I think 3 decimal places is accurate enough for most real life situations.