Calculus

Mean Value Theorem

Existence of point with average slope

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  • about 4 min
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abc≈1.95c≈1.96
a=0.5
b=3.5
f(b)−f(a)b−a=2.000=f′(c)\frac{f(b)-f(a)}{b-a} = 2.000 = f'(c)

Mean value theorem: on [a,b] there is at least one c where the tangent (pink) is parallel to the secant line (yellow).