Given F(x)=2x^3+4x^2-8x+2 determine:A. the intervals where f is increasing or decreeing.. B. local maxima and minima.c.the intervals where f is concave up or concave down d. points of inflection.e.graph the function (also try f(x)=x^3+3x^2, f(x)=x^3-12x)Attachment 1Attachment 224/ProjectGiven ( ) = ExRX8 * + 2 determina. The intervals where isincreasingFa De or decreediffBeing2 Annas 2Local Maximand Minime MaximaC . The intervals where is concaveor concave dowd. Points of inflection .ath the function .( Also try : flo = * + 3X " ) ( x ) = X – 12x )Find the linearization of the following functions(x ) = sink , at a16 for* of a = 4( x )3 be 25 4tax of X = 2CompareI’m onYand Ay for fix = 3 x + 2 x 2 + 2 x f2 40 to * = 201 on3.00 to * = 3.4use lineorization or the differential to approximate9 . 1 10b . 1 17 0$ 27 02 2 ) / 7.940STORolle’s Theorem 6 . Make aketch to illustrathe theoremc . show that the conditions of thetheorem are satisfiedfix = X – text – X – 1 on Ejl]d . Find c