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 66E
(a)
To determine
The domain of polynomial function P(x)=−3x6+2x5+9x4−8x3+11x2+4.
(b)
To determine
All the local minimum points of the polynomial P(x)=−3x6+2x5+9x4−8x3+11x2+4 and also find if there is any absolute minimum point.
(c)
To determine
All the local maximum points of the polynomial P(x)=−3x6+2x5+9x4−8x3+11x2+4 and also find if there is any absolute maximum point.
(d)
To determine
The range of polynomial function P(x)=−3x6+2x5+9x4−8x3+11x2+4.
(e)
To determine
All the intercepts of the polynomial P(x)=−3x6+2x5+9x4−8x3+11x2+4 nearest to the hundredth and also determine the y intercept analytically.
(f)
To determine
The open interval over which the function P(x)=−3x6+2x5+9x4−8x3+11x2+4 is increasing.
(g)
To determine
The open interval over which the function P(x)=−3x6+2x5+9x4−8x3+11x2+4 is decreasing.
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