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1.9.17 Concavity and the second derivative (A-level only)

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Question 40

The curve C has equation y=f(x)y = f(x)y=f(x), x>0x > 0x>0.

Given that

  • f′(x)=6x+Ax2+2f'(x) = \frac{6}{\sqrt{x}} + \frac{A}{x^2} + 2f′(x)=x​6​+x2A​+2, where AAA is a constant
  • f′′(x)=0f''(x) = 0f′′(x)=0 when x=9x = 9x=9
a.

Find the value of AAA.

[4]
b.

Given also that

  • f(x)=15f(x) = 15f(x)=15, when x=1x = 1x=1

Find f(x)f(x)f(x), giving each term in simplest form.

[4]

1.9.17 Concavity and the second derivative (A-level only) Questions

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