F(x)=2x²+18x+16
1) we have to calculate the first derived.
f´(x)=4x+18
2) Now, we equalize the first derived to "0" and find out the value of "x"
4x+18=0
4x=-18
x=-18/4=-4.5
3)we calculate the second derived
f´´(x)=4>0 ⇒we have a minimum at x=-4.5
4) Now we calculate the value of "y".
f(-4.5)=2(-4.5)²+18(-4.5)+16=40.5-81+16=-24.5
Therefore; Exist a minimum at (-4.5 , -24.5)
Answer: y = - 4x + 2
Explanation:
The graph shows a linear function, which is a first degree polynomial, whose form is ax + b.
The rule or fucntion is f(x) = y = ax + b. This form is called the slope-intercept form, because the coefficient a is the slope of the line and b is the y-intercept.
The graph permits you to calculate both parameters.
1) The slope, a is defined in this way:
- a = rise / run = [change in y] / [change in x] = [y₂ -y₁] / [x₂ - x₁]
- you can use the points (0, - 2) and (-1,2):
⇒ a = [ 2 - (-2) ] / [ -1 - 0 ] = 4 / (-1) = - 4
2) b, the y-intercept, is the value of the function, y, when x = 0. In the graph you can see that this is - 2. b = - 2.
3) Substituting the values of a and b in the form y = ax + b, you the rule:
8x^2-14xy+3y^2 is the answer
