Question

Question
f(x) = 2x^3 -3x^2 -12x+10 has
(a)
(b)
(c)
(d)
Minima at r= 2 and maxima at r=-1
Minima at r=-1 and maxima at x = 2
Minima at x =l and maxima at r= -2
Minima at x=2 and maxima at r=1​

Answer 1

$f(x) = 2 {x}^{3} - 3 {x}^{2} - 12x + 10$

$f ^{ \prime} (x) = 6 {x}^{2} - 6x - 12$

For critical Points:

${x}^{2} - x - 2 = 0$

$(x - 2)(x + 1) = 0$

$x = 2 \: \: \: \: and \: \: \: \: x = - 1$

$f ^{ \prime \prime} (x) = 12x - 6$

${f}^{ \prime \prime} (2) > 0$

$\boxed{\implies minima \: at \: x = +2} \\ \boxed{\implies maxima \: at \: x = - 1}$