Answer:
f(g) = -15x^2 + 15x + 2.
g(-2) = 18.
Step-by-step explanation:
f(g) = -5(3x^2 - 3x) + 2
= -15x^2 + 15x + 2.
g(-2) = 3(-2)^2 - 3(-2)
= 12 + 6
= 18.
Answer:
7.33
Step-by-step explanation:
I think c and b are correct answers
Given function:
![f(x)=xe^x](https://tex.z-dn.net/?f=f%28x%29%3Dxe%5Ex)
The minimum value of the function can be found by setting the first derivative of the function to zero.
![f^{\prime}(x)=xe^x+e^x](https://tex.z-dn.net/?f=f%5E%7B%5Cprime%7D%28x%29%3Dxe%5Ex%2Be%5Ex)
![\begin{gathered} xe^x+e^x\text{ = 0} \\ e^x(x\text{ + 1) = 0} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20xe%5Ex%2Be%5Ex%5Ctext%7B%20%3D%200%7D%20%5C%5C%20e%5Ex%28x%5Ctext%7B%20%2B%201%29%20%20%3D%200%7D%20%5Cend%7Bgathered%7D)
Solving for x:
![\begin{gathered} x\text{ + 1 = 0} \\ x\text{ = -1} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%5Ctext%7B%20%2B%201%20%3D%200%7D%20%5C%5C%20x%5Ctext%7B%20%3D%20-1%7D%20%5Cend%7Bgathered%7D)
![\begin{gathered} e^x\text{ = 0} \\ \text{Does not exist} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20e%5Ex%5Ctext%7B%20%3D%200%7D%20%5C%5C%20%5Ctext%7BDoes%20not%20exist%7D%20%5Cend%7Bgathered%7D)
Substituting the value of x into the original function:
![\begin{gathered} f(x=1)=-1\times e^{^{-1}}_{} \\ =\text{ -}0.368 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20f%28x%3D1%29%3D-1%5Ctimes%20e%5E%7B%5E%7B-1%7D%7D_%7B%7D%20%5C%5C%20%3D%5Ctext%7B%20-%7D0.368%20%5Cend%7Bgathered%7D)
Hence, the minimum value in the given range is (-1, -0.368)
Answer:
yes I believe so. best of luck