Answer:
Step-by-step explanation:
We can answer this in two ways: Differentiation and Graphing.
<u>Differentitate:</u>
The first derivative of a function yields a function that provides the slope for any point on the line of the original function. The slope of a vertex is zero, so we can set the first derivative to 0 and solve for x.
f(x) = 3(x-1)^2 + 4
f(x) = 3(x-1)(x-1) + 4
f(x) = 3(x^2 - 2x + 1) + 4
f(x) = 3x^2 - 6x + 7
f'(x) = 6x -6
Set this = 0 and find x:
0 = 6x -6
x = 1
The value of y when x=1 in the original equation is:
f(1) = 3(1-1)^2 + 4
y = 4
The vertex is (1,4)
<u>Graph:</u>
You can use DESMOS to plot the function. The result is attached. Look for the vertex and read the coordinates. (1,4) seems to work.
Answer:7.060 and 7.0600
Step-by-step explanation:0 doest not mean nothing
Answer:
Only one extreme value of f(x) is possible.
Step-by-step explanation:
We are given the quadratic function of independent variable x which is f(x) = x² - 7x - 6 ......(1)
Now. the condition for extreme values of f(x) is 
Hence, differentiating both sides of equation (1) with respect to x, we get
= 0
⇒ x = 3.5.
So there is only one value of x for which f(x) has extreme value which is x = 3.5.
Therefore, only one extreme value of the given function is possible. (Answer)
To find the length and width of 3 different rectangles that have an area of 48 square inches, you can use the factor pairs that result in 48.
The reason is that to find the area of a rectangle you multiply two dimensions.
2 in x 12 in
3 in x 8 in
4 in x 6 in
On all these either one could be the length and the other the width.
Answer:
1=x
Step-by-step explanation:
