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Level 2 Calculus , 2014 paper

Question 1d:
The graph of f(x)= -x^2 + kx - 5 has a turning point at (3,4)
Find the gradient of the function at the point where x=4.
Could you explain, please?

Kia ora @JOLM

A key thing that they do tell you in the question that it has a turning point at (3,4). There are two parts to answering this. Firstly to find the value of “k” based on the turning point. Secondly to find the gradient when x=4.

To find k we need to differentiate
f’(x) = -2x + k
Since there is a turning point at (3,4) if we sub x=3 into this it should equal zero

0 = -2(3) + k
0 = -6 + k
6 = k

Now that we have a value for k we can then find the gradient when x = 4

f’(4) = -2(4) + 6
f’(4) = -8 + 6
= -2

This would be a merit level question

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Great. Thank you for the clear explanation. It is much appreciated.

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