Formula Formula A function f(x) attains a local maximum 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 case, f(a) attains a local maximum value f(x) at x=a .
Chapter 3.5, Problem 62E
(a)
To determine
The domain of polynomial function P(x)=−2x5+7x4+x3−20x2+4x+16.
(b)
To determine
All the local minimum points of the polynomial P(x)=−2x5+7x4+x3−20x2+4x+16 and also to find if there is any absolute minimum point.
(c)
To determine
All the local maximum points of the polynomial P(x)=−2x5+7x4+x3−20x2+4x+16 and also to find if there is any absolute maximum point.
(d)
To determine
The range of polynomial function P(x)=−2x5+7x4+x3−20x2+4x+16.
(e)
To determine
All the intercepts of the polynomial P(x)=−2x5+7x4+x3−20x2+4x+16 nearest to the hundredth and also determine the y intercept analytically.
(f)
To determine
The open interval over which the function P(x)=−2x5+7x4+x3−20x2+4x+16 is increasing.
(g)
To determine
The open interval over which the function P(x)=−2x5+7x4+x3−20x2+4x+16 is decreasing.
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