MAT - Paper 2011 - Q3
Flashcards
What has to be true about the straight line’s gradient $m$ and the derivative of the cubic at the point where they just touch?
What has to be true about the straight line’s gradient $m$ and the derivative of the cubic at the point where they just touch?They must be equal.
For a straight line
\[y = mx + c\]and a general function $f(x)$ What must be true for the line to ‘touch’ the function at point $a$??
\[m = f'(a)\] If you pull $A$ all the way back to $-10^6$, what will happen to the point where the line touches the cubic?
If you pull $A$ all the way back to $-10^6$, what will happen to the point where the line touches the cubic?It will get closer and closer to the local maximum.
If
\[A = -1\]
Why must the value of $B$ also be $-1$?? Because the line and cubic only touch once, and the cubic goes through $(-1, 0)$.
Visually, what would you do the value of $A$ to push up the area in region $R$?
Visually, what would you do the value of $A$ to push up the area in region $R$?Move it closer and closer to $-1$.
You’re stuck trying to mathematically describe some function you’re trying to optimise in order to find the best or worst value of some constant. What should you do try and do to make some progress?
Switch to thinking intuitively or visually.
You’ve been asked to prove something given, but you’re stuck showing that it’s true. What should you do to try and make some progress?
Take what they’ve given you and substitute it into the problem to see why it works.