Question

sketch a graph of the function f(x) = x3 + 2x2 – 8x.

Answer 1

Answer:

x < - 4  f(x) is -ve

-4 < x < 0  f(x) is + ve

0 < x < 2 f(x) is -ve

x > 2  f(x) is +ve

Step-by-step explanation:

f(x) = x³ + 2x² - 8x

= x(x² + 2x -8)

= x( x² + 4x - 2x -8)

=x(x(x+4) -2(x+4))

=x(x-2)(x+4)

Zeroes are

0 , 2 , - 4

x < - 4  f(x) is -ve

-4 < x < 0  f(x) is + ve

0 < x < 2 f(x) is -ve

x > 2  f(x) is +ve