1.

Find the points of local maxima and local minima for the following functions. Also find respective maximum and minimum values. (i) y=x^(4)-14x^(2)+24x-3 (ii) y=((x+1)(x+4))/((x-1)(x-4)) (iii) y=x (x-1)^(2) (x+1)^(2) (iv) y=(log x)//x y=e^(x) sin x" in "[-pi,pi] y=sin x+cos x" in "[0,2pi]

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Answer :(i) max (1,8 ), min (-3 ,-120) and (2,5)
(i) max : (2,-9) and min (-2,-1/9)
(iii) `max (1/SQRT5): (16sqrt5)/(125) and (-1,0): " min "(-1)/sqrt5, -(16sqrt5)/(125), (1,0)`
(iv) `max (E 1/e) `
v `max ((3pi)/(4), (1)/sqrt2 e^(3pi//4)) min ((-pi)/(4), (-1)/(sqrt2), e^(-pi//4))`


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