The product of three point five and a number v
There are four types of transformations of an image on a graph: translation, rotation, reflection, and dilation.
If the image moved across the graph without changing its shape, form, or tilt, it is a translation. Basically without changing form it slid from one place to another.
If the image rotated across the graph, such as switching upside-down from the first quadrant to the second, it is a rotation.
If the image moved across the graph and is in the exact opposite form as it started in (like a mirror,) it is a reflection.
If the image grew larger, it is a dilation.
Just follow the pre-image (f(x)=3x, since it started there,) to the image on your graph (g(x), since it ended there) to find out which transformation it is.
<span>they are perpendicular.</span>
Answer:
one
Step-by-step explanation:
The minimum value of f(4) - f(1) is <u>6</u>.
The maximum value of f(4) - f(1) is <u>12</u>.
In the question, we are given that, 2 ≤ f'(x) ≤ 4 for all values of x.
Taking the given inequality as (i).
We are asked to find the minimum and maximum possible values of f(4) - f(1).
We multiply (i) by dx throughout, to get:
4dx ≤ f'(x)dx ≤ 5dx.
To find this, we integrate (i) in the definite interval [4, 1] with respect to dx, to get:
![\int_{1}^{4}2dx \leq \int_{1}^{4}f'(x)dx \leq \int_{1}^{4}4dx\\\Rightarrow [2x]_{1}^{4} \leq [f(x)]_{1}^{4} \leq [4x]_{1}^{4}\\\Rightarrow 2*4 - 2*1 \leq f(4)-f(1) \leq 4*4 - 4*1\\\Rightarrow 6 \leq f(4) -f(1) \leq 12](https://tex.z-dn.net/?f=%5Cint_%7B1%7D%5E%7B4%7D2dx%20%5Cleq%20%5Cint_%7B1%7D%5E%7B4%7Df%27%28x%29dx%20%5Cleq%20%5Cint_%7B1%7D%5E%7B4%7D4dx%5C%5C%5CRightarrow%20%5B2x%5D_%7B1%7D%5E%7B4%7D%20%5Cleq%20%5Bf%28x%29%5D_%7B1%7D%5E%7B4%7D%20%5Cleq%20%5B4x%5D_%7B1%7D%5E%7B4%7D%5C%5C%5CRightarrow%202%2A4%20-%202%2A1%20%5Cleq%20f%284%29-f%281%29%20%5Cleq%204%2A4%20-%204%2A1%5C%5C%5CRightarrow%206%20%5Cleq%20f%284%29%20-f%281%29%20%5Cleq%2012)
Thus, the minimum value of f(4) - f(1) is 6.
The maximum value of f(4) - f(1) is 12.
Learn more about definite integrals at
brainly.com/question/17074932
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