Find the intercepts and relative extrema for the graph of each function. 1. f(x)=1/4(x+2)(x-1)^2 2. h(x)=2x^3+5x^2-25x

Definition:

x -intercept : The point where the graph crosses the x-axis

Substitute in y=0 and solve for x

y-intercept : The point where the graph crosses the y-axis

Substitute in x=0 and solve for f(x) or y

1.

Given the function f(x) =       .....[1]

to find x-intercept;

substitute y= 0 in equation [1];

⇒ x+2 = 0 and

⇒ x =-2 and x= 1

Therefore, the x-intercept are; (-2,0) and (1 ,0)

Similarly, for y-intercept

Substitute x=0 in [1] to solve for y;

⇒

Simplify;

y =

therefore, the y-intercept is, (0, )

To find the relative extrema for the function f(x) = ;

Relative Extrema states that when the graph is turning around then there must be a horizontal tangent at that point,  also we can say that  the derivative value will be zero at that point, because a horizontal tangent has slope equal to 0.

As you can see in the Figure 1

Relative extrema of the function f(x) are (-1,1) and (1,0)

2.

Given the function h(x) =     .....[2]

to find x-intercept;

substitute y= 0 in equation [2];

 or

or

Simplify:

x =0, x=-5 and

Therefore, the x-intercept are; (0,0), (-5,0) and (,0)

Similarly, for y-intercept

Substitute x=0 in [2] to solve for y=h(x);

h(x) =    

h(x) =0

therefore, the y-intercept is, (0,0)

To find the relative extrema for the function  h(x) =

Relative Extrema states that when the graph is turning around then there must be a horizontal tangent at that point,  also we can say that  the derivative value will be zero at that point, because a horizontal tangent has slope equal to 0.

As you can see in the Figure 2

Relative extrema of the function h(x) are  (-3.038, 66.019) and (1.371, -19.723)

-4

step-by-step explanation:

(-4+8)=-(4-8)=-8+4=-4