Answer:
f(x) = - 8
Explanation:
The given function is
f(x) =2x^2 -4x -6
The first step is to find the derivative of the function. Recall, if
y = ax^b
y' = abx^(b - 1)
Thus,
f'(x) = 4x - 4
We would equate f'(x) to zero and solve for x. We have
4x - 4 = 0
4x = 4
x = 4/4
x = 1
We would substitute x = 1 into the original function and solve for f(x) or y. It becomes
f(1) =2(1)^2 -4(1) - 6 = 2 - 4 - 6
f(1) = - 8
Thus, the minimum value is f(x) = - 8
Answer:
i need pointsss
Step-by-step explanation:
See the attached figure.
<span>f(x)=-2x−3 ⇒⇒ black graph ⇒⇒ range = R
</span>
<span>g(x)=-2|x+3|−3 ⇒⇒ red graph ⇒⇒ range = </span><span>{y∣y ≤ -3}
</span>
<span>h(x)=-2(x−4)²+3 ⇒⇒ blue graph ⇒⇒ </span><span>range = {y∣y ≤ 3}
</span>
<span>j(x)=-2x³+3x²+x−1
⇒⇒ green graph </span>⇒⇒ range = R
∴ <span>
The function which has a range of {y∣y ≤ 3} is </span><span>
h(x)=-2(x−4)²+3
</span>
<span>
</span>
Which is the third choice<span>
</span>
Answer:
1
Step-by-step explanation:
Slope is y2-y1 over x2-x1
So:
4-2 = 2
-1+3= 2
so the slope here is 2/2 which we can simplify to 1
Given that the equation of the line is ![2x+5y=-6](https://tex.z-dn.net/?f=2x%2B5y%3D-6)
We need to determine the x and y intercepts.
<u>The coordinates of y - intercept:</u>
The y - intercept of the equation is the value of y when x = 0.
Thus, substituting x = 0 in the equation
, we get;
![2(0)+5y=-6](https://tex.z-dn.net/?f=2%280%29%2B5y%3D-6)
![5y=-6](https://tex.z-dn.net/?f=5y%3D-6)
![y=-\frac{6}{5}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B6%7D%7B5%7D)
Thus, the coordinates of the y - intercept are ![(0,-\frac{6}{5})](https://tex.z-dn.net/?f=%280%2C-%5Cfrac%7B6%7D%7B5%7D%29)
<u>The coordinates of the x - intercept:</u>
The x - intercept of the equation is the value of x when y = 0.
Hence, substituting y = 0 in the equation
, we get;
![2x+5(0)=-6](https://tex.z-dn.net/?f=2x%2B5%280%29%3D-6)
![2x=-6](https://tex.z-dn.net/?f=2x%3D-6)
![x=-3](https://tex.z-dn.net/?f=x%3D-3)
Thus, the coordinates of the x - intercept is ![(-3,0)](https://tex.z-dn.net/?f=%28-3%2C0%29)