(a) Find the first derivative of $y$ at $x = 6$, given that : | $x$ |…

Question

(a) Find the first derivative of $y$ at $x = 6$, given that :

| $x$ | $y$ |

|---|---|

| 4.5 | 9.69 |

| 5 | 12.9 |

| 5.5 | 16.71 |

| 6.0 | 21.18 |

| 6.5 | 26.37 |

| 7.0 | 32.34 |

(b) Using Regula falsi method, find a real root of the equation : $x \log_{10} x = 1.2$

(c) Evaluate $y(0.2)$ by Runge-Kutta method of 4th order, given that : $y' = x^2 - y^2$ with $y(0) = 1$.