Calculus Curve Sketching Rational Function MCV4U
#globalmathinstitute #anilkumarmath Curve Sketching for Radical Function with First Derivative: • Curve Sketching f(x)=x^(1/3) (x-4)^(2...
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Application Derivatives of Exponential and Logarithms: • Derivatives Exponential Trigonometric...
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Critical number is the point where the derivative is zero or undefined. Maximum occurs where the derivative changes from positive to negative. Minimum is at the point where the first derivative changes from negative to positive increasing to decreasing. Minimum is at a point where the derivative changes from decreasing to increasing. Second derivative can be used to confirm maximum or minimum at the critical point. Positive second derivative means minimum and negative means maximum.
Graph Rational Function
Describe characteristics
Find interval of increase (-3, 0), (0, 3)
Interval of decrease x less than -3, x greater than 3
local Maxima (3, 2/9)
Local Minimum (-3, -2/9)
Find interval of concavity
Concave Up (-3sqrt2, 0), x greater than 3 sqrt2
Find point of inflection: x = -3sqrt2, 3sqrt2, 0
Sketch the curve
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