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 $a$??
\[m = f'(a)\]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 $a$?
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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 $(-1, 0)$.
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 $-1$?
IfBecause 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 $-1$.