MediumDerivatives

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §1.2 Calculus Without Limits, #24 · Calculus · Derivatives

True (with reason) or false (with example)

This problem involves numbers $f_{0}, f_{1}, f_{2}, \dots$ and their differences $v_{j} = f_{j} - f_{j - 1}$ . They give practice with subscripts $0, \dots, j$ .

True (with reason) or false (with example).
(a) When the $f$ 's are increasing so are the $v$ 's.
(b) When the $v$ 's are increasing so are the $f$ 's.
(c) When the $f$ 's are periodic so are the $v$ 's.
(d) When the $v$ 's are periodic so are the $f$ 's.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §1.2 Calculus Without Limits, #24

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