Question

Let it be f (x) = 2x³ - 9x² - 10.

a) specify the zeros of the f derivate of the function.

b) with what variable x values does f on grow?

c) determine between the maximum and the minimum value of the function f and [-4, 4].

Answer 1

a)

$f'(x)=6x^2-18x=0$

$x(6x-18)=0$

$x_1=0,x_2=3$

b)

f(x) grows is f'(x) > 0

$x(6x-18)>0$

$x<0$ and $x>3$

c)

at $x=3$ function has local minimum (f'(x) changes from "-" to "+")

$f(3)=-37$

$f(-4)=-282$

$f(4)=-26$

so, minimum -282 and maximum is -26 at [-4,4]