Let f be differentiable on [a,b] and suppose that k is a number between f'(a) and f'(b). Then there exists a point c ε (a,b) such that f'(c)=k.
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GREEN'S THEOREM: if m=m(x,y) and n= n(x,y) are the continuous functions and also partial differential in a region 'r' of x,y plane bounded by a simple closed curve c. DIVERGENCE THEOREM: if f is a vector point function having continuous first order partial derivatives in the region v bounded by a closed curve s
A cubic has from 1 to 3 real solutions. The fact that every cubic equation with real coefficients has at least 1 real solution comes from the intermediate value theorem. The discriminant of the equation tells you how many roots there are.
derivatives are the functions required to find the turning point of curve
They are derivatives with respect to measures in space: normally length, area or volume.
Yes.