# Question #020d3

Mar 20, 2017

$y = 10 \sqrt{x} + 3$

#### Explanation:

In math-speak you have:

$y ' = \frac{\alpha}{\sqrt{x}}$ where $\alpha$ is some constant

Compared to your other stuff, This is simple power rule material:

$\int {x}^{n} \mathrm{dx} = \frac{{x}^{n + 1}}{n + 1} + C$

It solves as:

$y = 2 \alpha \sqrt{x} + \beta$

• Applying the $\left(0 , 3\right)$ condition:

$3 = 0 + \beta \implies \beta = 3$

• Applying the $\left(4 , 23\right)$ condition:

$23 = 2 \alpha \cdot \left(\pm 2\right) + 3 \implies \alpha = \pm 5$

$\implies y = \pm 10 \sqrt{x} + 3$

But it has to go through $\left(4 , 23\right)$ so it is:

$\implies y = 10 \sqrt{x} + 3$