Answered: For the function f(x) = 4+ 12x² − x³,…

For the function f(x) = 4+ 12x² − x³, find the local extrema. Then, classify the local extrema using the second derivative test.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.4: Definition Of The Derivative

Problem 36E

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PS. Be sure to state the second derivative values at the extrema. and the (x,y) value for the local minima and local maxima (Points)

For the function f(x) = 4+ 12x²-x³, find the local extrema. Then, classify the local extrema using the
second derivative test.

Formula Formula A function f ( x ) is also said to have attained a local minimum at x = a , if there exists a neighborhood ( a − δ , a + δ ) of a such that, f ( x ) > f ( a ) , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a f ( x ) − f ( a ) > 0 , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a In such a case f ( a ) is called the local minimum value of f ( x ) at x = a .

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