MAT - Paper 2011 - Q3


Flashcards

PHOTO MAT 2011 Q3 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 $a$?


\[m = f'(a)\]

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PHOTO MAT 2011 Q3

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 $(-1, 0)$.

PHOTO MAT 2011 Q3 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.

PHOTO MAT 2011 Q3 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 $(-1, 0)$.

PHOTO MAT 2011 Q3 Visually, what would you do the value of $A$ to push up the area in region $R$?


Move it closer and closer to $-1$.




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