(a) find the x- coordinate of each relative maximum and relative minimum point o

Question

(a) find the x- coordinate of each relative maximum and relative minimum point of f.( First derviative test)

(b) Find the x-coordinate of each inflection point of f. (f" quoitient rule)

(c) Find the absolute maximum value of f(x) ( use radical form)

Explanation / Answer

df(x)/dx= 4x/(x^2+3) -1 equating to 0 we get, x^2+3-4x =0 x^2 -3x -x +3 =0 =>(x-3)(x-1) => x=1,3 are the relative extreme points. (b) d^2f(x)/dx = [(x^2 + 3) *4 - (4x)*(2x)] /(x^2 + 3)^2 =>4x^2 + 12 - 8x^2 =0 =>x = ± v3 are the point of inflection (c)f(1) = 2 ln4 - 1 = 1.7726 f(3) = 2ln12 - 3 = 1.9698 f(-3) = 2ln12 + 3 = 7.9698 f(5) = 2ln28 - 5 = 1.6644 => absolute maximum = f(-3) = 7.9698 and absolute minimum= f(5)=1.6644

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