Question

can anyone please help me with this?

The elevation of a hiking trail is modelled by the function h(x)=2x^3+3x^2−17x+12 where h is the height in meters above sea level and x is the horizontal distance from a ranger station in kilometers. If x<0, the position is to the west of the station, and if x>0 the position is to the east. Since the trail extends 4.2km to the west of the ranger station and 4km to the east, the model is accurate for {xεR|−4.2≤x≤4}. How can we determine which sections of the trail are above sea level?

Answer 1

Answer:

a) $x > 1.5$

b) $-4 < x < 1$

Step-by-step explanation:

Given that function is a third order polynomial, it can be factorized:

$h(x) = (x+4)\cdot (x-1.5)\cdot (x -1)$

The following inequation must be analyzed to determine which sections are above sea level:

$(x+4)\cdot (x-1.5)\cdot (x-1) >0$

By Algebra, it is known that product between three positive numbers or two negative numbers and a positive number are equal to a positive number. Then, there are only two trails:

a) $x > 1.5$

b) $-4 < x < 1$