A function f(x) = 1 - x² + x³ is defined in the closed interval [-1, 1]. The value of x in the open interval (-1, 1) for which the mean value theorem is satisfied, is

A. 1 B. -1 C. 0 D. Limit does not exit

A. 2 + 3x - x² - \[\frac{{{{\text{x}}^3}}}{2}\] + ... B. 2 - 3x + x² - \[\frac{{{{\text{x}}^3}}}{2}\] + ... C. 2 + 3x + x² + \[\frac{{{{\text{x}}^3}}}{2}\] + ... D. 2 - 3x - x² + \[\frac{{{{\text{x}}^3}}}{2}\] + ...

A. 0 B. \[\infty \] C. \[\frac{1}{2}\] D. \[ - \infty \]

A. \[1 + \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\] B. \[ - 1 - \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\] C. \[1 - \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\] D. \[ - 1 + \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]