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1 Unit 1: Pure Mathematics A

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Question 290

The curve with equation y=f(x),x>0y = \mathrm{f}(x), x > 0y=f(x),x>0, passes through the point P(9,−5)P(9, -5)P(9,−5).

Given that

dydx=2xx−12x−12 \frac{\mathrm{d} y}{\mathrm{d} x} = 2x\sqrt{x} - 12x^{-\frac{1}{2}} dxdy​=2xx​−12x−21​
a.

Find the equation of the tangent to the curve at PPP, writing your answer in the form y=mx+cy = mx + cy=mx+c, where mmm and ccc are integers to be found.

[4]
b.

Find f(x)f(x)f(x).

[5]
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1 Unit 1: Pure Mathematics A Questions

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