Question 2

a. Verify Rolle's theorem in the case of function $f(x) = 2x^3 + x^2 - 4x - 2$. (4 marks)

b. If $\dfrac{x^2}{a^2+u} + \dfrac{y^2}{b^2+u} + \dfrac{z^2}{c^2+u} = 1$, then prove that$$u_x^2 + u_y^2 + u_z^2 = 2\left(x u_x + y u_y + z u_z\right).$$ (4 marks)