1.9.20 Integrate kx^n

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

Given that

\frac{\mathrm{d} y}{\mathrm{d} x} = 2x\sqrt{x} - 12x^{-\frac{1}{2}}

a.

Find the equation of the tangent to the curve at $P$ , writing your answer in the form $y = m x + c$ , where $m$ and $c$ are integers to be found.

[4]

b.

Find $f (x)$ .

[5]

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

Given that

\frac{\mathrm{d} y}{\mathrm{d} x} = 2x\sqrt{x} - 12x^{-\frac{1}{2}}

a.

Find the equation of the tangent to the curve at $P$ , writing your answer in the form $y = m x + c$ , where $m$ and $c$ are integers to be found.

[4]

b.

Find $f (x)$ .

[5]

1.9.20 Integrate kx^n Questions