Answer to Question #107073 in Real Analysis for Garima Ahlawat

Question #107073
(1) for the function f , defined by f(x) = 4x^3 - 4x^2 -7x -2 , there exist a point c €]-1/2 ,2[ satisfying f'(c) = 0
(2) for all even integral values of n, lim (x+1)^-n as x tends to infinity exists.
1
Expert's answer
2020-04-02T08:04:52-0400

1) "f'=12x^2-8x-7"

"f'=0\\iff x_1=-\\frac{1}{2}; x_2=\\frac{7}{6}"

both points are in the interval ["-\\frac{1}{2};2" ]

2) "\\lim\\limits_{x\\to \\infty}(x+1)^{-n}=\\left\\{\\begin{matrix}\n 0 & n>0 \\\\\n 1 & n=0 \\\\\n\\infty& n<0\n\\end{matrix}\\right."

the limit doesn't exist for all negative n


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