Master Fractional Calculus: The
Complete 2025/2026 Study Guide for
'Fractional Deterministic and
Stochastic Calculus', 1st Edition by
Giacomo Ascione, Yuliya Mishura,
and Enrica Pirozzi. Ace Your Exams
First Try!
Formal definition of derivative - CORRECT ANSWERSlim x→∞[f(x+h)-f(x)]/h
Alternate definition of derivative - CORRECT ANSWERSlim x→a[f(x)-f(a)]/(x-a)
When f '(x) is positive, f(x) is - CORRECT ANSWERSincreasing
, When f '(x) is negative, f(x) is - CORRECT ANSWERSdecreasing
When f '(x) changes from negative to positive, f(x) has a - CORRECT
ANSWERSrelative minimum
When f '(x) changes from positive to negative, f(x) has a - CORRECT
ANSWERSrelative maximum
When f '(x) is increasing, f(x) is - CORRECT ANSWERSconcave up
When f '(x) is decreasing, f(x) is - CORRECT ANSWERSconcave down
When f '(x) changes from increasing to decreasing or decreasing to increasing, f(x) has
a - CORRECT ANSWERSpoint of inflection
When is a function not differentiable - CORRECT ANSWERScorner, cusp, vertical
tangent, discontinuity
Chain Rule - CORRECT ANSWERSf '(g(x)) g'(x)
Particle is moving to the right/up - CORRECT ANSWERSvelocity is positive
Particle is moving to the left/down - CORRECT ANSWERSvelocity is negative
absolute value of velocity - CORRECT ANSWERSspeed
y = sin⁻¹(x), y' = - CORRECT ANSWERSy' = 1/√(1 - x²)
y = cos⁻¹(x), y' = - CORRECT ANSWERSy' = -1/√(1 - x²)
y = tan⁻¹(x), y' = - CORRECT ANSWERSy' = 1/(1 + x²)
y = cot⁻¹(x), y' = - CORRECT ANSWERSy' = -1/(1 + x²)
y = a^x, y' = - CORRECT ANSWERSy' = a^x ln(a)
y = ln(x), y' = - CORRECT ANSWERSy' = 1/x
y = log (base a) x, y' = - CORRECT ANSWERSy' = 1/(x lna)
To find absolute maximum on closed interval [a, b], you must consider... - CORRECT
ANSWERScritical points and endpoints
mean value theorem - CORRECT ANSWERSif f(x) is continuous and differentiable,
slope of tangent line equals slope of secant line at least once in the interval (a, b)
Complete 2025/2026 Study Guide for
'Fractional Deterministic and
Stochastic Calculus', 1st Edition by
Giacomo Ascione, Yuliya Mishura,
and Enrica Pirozzi. Ace Your Exams
First Try!
Formal definition of derivative - CORRECT ANSWERSlim x→∞[f(x+h)-f(x)]/h
Alternate definition of derivative - CORRECT ANSWERSlim x→a[f(x)-f(a)]/(x-a)
When f '(x) is positive, f(x) is - CORRECT ANSWERSincreasing
, When f '(x) is negative, f(x) is - CORRECT ANSWERSdecreasing
When f '(x) changes from negative to positive, f(x) has a - CORRECT
ANSWERSrelative minimum
When f '(x) changes from positive to negative, f(x) has a - CORRECT
ANSWERSrelative maximum
When f '(x) is increasing, f(x) is - CORRECT ANSWERSconcave up
When f '(x) is decreasing, f(x) is - CORRECT ANSWERSconcave down
When f '(x) changes from increasing to decreasing or decreasing to increasing, f(x) has
a - CORRECT ANSWERSpoint of inflection
When is a function not differentiable - CORRECT ANSWERScorner, cusp, vertical
tangent, discontinuity
Chain Rule - CORRECT ANSWERSf '(g(x)) g'(x)
Particle is moving to the right/up - CORRECT ANSWERSvelocity is positive
Particle is moving to the left/down - CORRECT ANSWERSvelocity is negative
absolute value of velocity - CORRECT ANSWERSspeed
y = sin⁻¹(x), y' = - CORRECT ANSWERSy' = 1/√(1 - x²)
y = cos⁻¹(x), y' = - CORRECT ANSWERSy' = -1/√(1 - x²)
y = tan⁻¹(x), y' = - CORRECT ANSWERSy' = 1/(1 + x²)
y = cot⁻¹(x), y' = - CORRECT ANSWERSy' = -1/(1 + x²)
y = a^x, y' = - CORRECT ANSWERSy' = a^x ln(a)
y = ln(x), y' = - CORRECT ANSWERSy' = 1/x
y = log (base a) x, y' = - CORRECT ANSWERSy' = 1/(x lna)
To find absolute maximum on closed interval [a, b], you must consider... - CORRECT
ANSWERScritical points and endpoints
mean value theorem - CORRECT ANSWERSif f(x) is continuous and differentiable,
slope of tangent line equals slope of secant line at least once in the interval (a, b)
