Differentiability and the mean value theorems
General · Mathematics
Study notes
Q: f(x) = x² on [1,3]. Find c with f'(c) = (f(3)-f(1))/(3-1). (f(3)-f(1))/2 = (9-1)/2 = 4. f'(x) = 2x: 2c = 4: c = 2 ∈ (1,3) ✓! (Tangent parallel to secant - MVT guarantees!)