Let f(x) = x3+3x2 - 9x+2. Then, f(x) has _________________ .

Question

KollegeApply · Accepted Answer

ext { a minimum at x = 1} 	ext { Given }: f\left( x ight) = x^3 + 3 x^2 - 9x + 2 \Rightarrow f'\left( x ight) = 3 x^2 + 6x - 9 	ext { For a local maxima or a local minima, we must have } f'\left( x ight) = 0 \Rightarrow 3 x^2 + 6x - 9 = 0 \Rightarrow x^2 + 2x - 3 = 0 \Rightarrow \left( x + 3 ight)\left( x - 1 ight) = 0 \Rightarrow x = - 3, 1 	ext { Now,} f''\left( x ight) = 6x + 6 \Rightarrow f''\left( 1 ight) = 6 + 6 = 12 > 0 	ext { So, x = 1 is a local minima } . 	ext { Also }, f''\left( - 3 ight) = - 18 + 6 = - 12 < 0 	ext { So, x = - 3 is a local maxima } .

AChoose Your Answer