Max(g(x)) = g(π/2) = 2
Max(h(x)) = h(5) = 3
Of these values, f(3) = 4 is the largest.
The function with the largest maximum is f(x).
The correct option is 1. The function f(x) has the largest maximum.
The vertex form of a parabola is
Where, (h,k) is vertex.
The given functions is
Here, a=-1, h=-5 and k=3. Since the value of a is negative, therefore it is an downward parabola and vertex is the point of maxima.
Thus the maximum value of the function h(x) is 3.
The value of cosine function lies between -1 to 1.
Multiply 4 on each side.
Subtract 2 from each side.
Therefore the maximum value of the function g(x) is 2.
From the given table it is clear that the maximum value of the function f(x) is 4 at x=3.
Since the function f(x) has the largest maximum, therefore the correct option is 1.
people in Africa. African nations typically fall toward the bottom of any list measuring small size economic activity, such as income per capita or GDP per capita, despite a wealth of natural resources
1) The first way is graphing. You can find the maximum value visually by graphing the equation and finding the maximum point on the graph
2) The second way to determine the maximum value is using the equation y = ax² + bx + c.
If your equation is in the form ax² + bx + c, you can find the maximum by using the equation:
max/min = c - (b2 / 4a).
The first step is to determine whether your equation gives a maximum or minimum. This can be done by looking at the x² term.
If x²>0 > the vertex point will be a minimum.
If x²<0> the vertex will be a maximum.
3)There's one more way to determine the maximum value of a function, and that is from the equation:
y = a(x - h)2 + k
If the a term in this equation must be negative for there to be a maximum.
If the a term is negative, the maximum can be found at k. No equation or calculation is necessary - the answer is just k.
using a graph tool
see the attached figure
the maximum value of f(x) is 1 at the point (2,1)
the maximum value of g(x) is 4 at the point (-2,4)
the answer isThe function g(x) has the greater maximum value
To find the vertex (h,k) (where h=x-coordinate and k=y-coordinate) of a quadratic function of the form we'll use the vertex formula: , and then we are going to replace that value in our original function to find k.
So, in our function , and .
Lets replace those values in our vertex formula:
Now that we know the x-coordinate of our vertex, lets replace it in the original function, to get the y-coordinate:
We just prove that the vertex of is (2,1), and for the graph we can tell that the vertex of is (-2,4). The only thing left is compare their y-coordinates to determine which one has the greater maximum value. Since 4>1, we can conclude that has the greater maximum.