Mathematics I20745 marksNumerical: mean value theoremMean value theorem
Verify Mean value theorem of f(x) = x3 - 3x + 3 for [-1,2].
Verify Mean value theorem of $f(x) = x^3 - 3x + 3$ for [-1,2]. [5]
- Function: $f(x) = x^3 - 3x + 3$ - Interval: $[a, b] = [-1, 2]$, so $a = -1$, $b = 2$ If $f$ is continuous on $[a,b]$ and differentiable on $(a,b)$, then there exists $c \in (a,b)$ such that: $$f'(c) = \frac{f(b) - f(a)}{b - a}$$ $f(x)$ is a polynomial, hence: - Continuous on $[-1, 2]$ ✓ - Diffe...