Question

Graph the polynomial using calculus methods.

F(x)= 7/3 x³ + 13/2 x² -12x +3

List local extrema, intervals of concavity, and inflection point(s) if they exist.

Local maximum:

Local Minimum:

Concave up:

Concave down:

Inflection point(s):

Answer 1

132 We have Foi = 7 x² + 13 x ² - 12x + 3 Derivating by using thxh = nxhi F') = 7 (3x 3-1) + 13 (2 x ²-1) -12 (15²) + 3x0 7x²+ 130-12 agan deneating F") = 14 2+13 find out cntikal points where f'x=0 -) 7?+ 137-12 = 0 By quadratic Formula - 13 ) + 4670(-12) 2(7) =) x = 0.676586 -2.53373 How checking sign of foci over these pount at x= 0.676586 ) 20 so it & point of local minima local minimum value f(0.676586) = – 1.42086 at x = -2.5 3373 fxILO so here local maxim local maximum value f€ 2.5 3373) = 37.18 Now set f'ol) = 0 for inflection points 14x + 13 = 0 -- 13 /

10513 588 17.88 (1, 17-88) FO down reflection point Flow checking sign of frees over it =) cóncave up on (-13,00) here f(x) > 0 - concave down on (-20, -13 ) hese fxl< ممال tx=0-677 X=-2.834 x=-113 14