MAT - Paper 2009 - Q3

Created: October 13, 2021

Flashcards

2021-10-13

What trick can you use for sketching $f(x)^2$?

Lightly sketch $f(x)$ and then make sure it’s positive and increase all the gradients.

PHOTO POLYNOMIAL If this is $f(x)$, what does the graph of $f(x)^2$ look like?

PHOTO POLYNOMIAL SQUARED

We are given

\[3n^2 - n - B + 3Bn \ge 4An^2 - An\]

for all $n > 1$. Equivalently

\[(3 - 4A)n^2 + (A + 3B - 1)n - B \ge 0\]

Why can you show that

\[3 - 4A \ge 0 \implies A \le 3/4\]

here?

Because if it $A \le 3/4$ there would be a negative for the $n^2$ term and so negative for large $n$.

\[-ax^2 + bx + c\]

where $a, b, c > 0$. What is ALWAYS true about this function for large values of $n$?

It is negative.



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