Question

Determine which statements are true about the extrema of the graphed to fourth degree Polynomial. Select all that apply.

Answer 1

Refer answer below

Explanation:

Given is a graph in the interval (-infinity, infinity).

From the graph we observe that it is continuous graph.

The curve is decreasing for x <-2 and increases for (-2,1) and again decreases from (1,3) then increases from (3,infinity)

Hence f'(x) >0 for (-2,1) and (3,infinity)

f'(x) <0 for (-infty, -2) and (1,3)

From the above we find that f'(x) =0 for x=-2,1,and 3

Extreme points are -2,1 and 3

Absolute and local minima at x=-2, y=-9.67

Local maxima at (1,6.08) and again

local minima at (3,0.75)

Absolute maxima lies at infinity

Answer 2

Option 4. overall minimum in (-2.9.67)

Explanation:

A global maximum point (x0, f (x0)) is defined as the point at which f (x0) is the maximum value of the function. That is, there is no value in the domain of f (x) other than x0 where f (x) is greater than f (x0)

A global minimum point (x0, f (x0)) is defined as the point at which f (x0) is the smallest value of the function. That is, there is no value in the domain of f (x) other than x0 where f (x) is less than f (x0)

Based on that deficion we must look for the point where f (x) has the lowest value.

That point is (-2.9.67)

Therefore that is the overall minimum of the function.

Although the function has a maximum in (1.6.08), the function keeps growing for x> 4, that means that there is a point where the function is bigger than in x = 1.

Therefore this is not a local maximum.