Which of the following functions grows the fastest as x grows without bound?
f(x)=x^2
g(x)=x^2+5x <<<<MY ANSWER
h(x)=(sqrt x^4+2x)
They all grow at the same rate
Compare the growth rate of the functions f(x)=4^x and g(x)=(sqrt 16^x+2^x)
f(x) grows faster than g(x)
g(x) grows faster than f(x)MY ANSWER
f(x) and g(x) grow at the same rate
it cannot be determined
There is a graph that starts at (-4,0) it then goes to (-2,-2) it goes through (0,0) as it goes to (2,2) and ends at (4,0)
Where is this graph concave up?
(-4,-2) U (2,4)
(-2,2) MY ANSWER
(-4,0)
(0,4)
Thank you!
The graph is concave up at the point (-2,2).
To determine which function grows the fastest as x grows without bound, we can analyze the growth rates of all the functions listed.
First, let's compare the functions f(x) = x^2, g(x) = x^2 + 5x, and h(x) = √(x^4 + 2x).
The growth of a function can be determined by examining the highest power of x in the equation. In this case, f(x) has a power of 2, g(x) has a power of 2, and h(x) has a power of 4.
Since h(x) has the highest power, we can conclude that h(x) grows the fastest as x grows without bound.
Therefore, the correct answer is: h(x) = √(x^4 + 2x).
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Let's now analyze the growth rates of the functions f(x) = 4^x and g(x) = √(16^x + 2^x).
To compare the growth rates, we can observe the exponential nature of the functions. f(x) = 4^x represents exponential growth, where the base is 4, and g(x) = √(16^x + 2^x) includes both an exponent and a root.
To determine which function grows faster, we need to consider the bases of the exponentials. In this case, f(x) has a base of 4, and g(x) has bases of both 16 and 2.
Since 16 > 4 and 2 > 4, we can infer that g(x) has a higher growth rate than f(x).
Therefore, the correct answer is: g(x) = √(16^x + 2^x).
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To identify the intervals where a graph is concave up, we need to examine the signs of the second derivative of the function.
The graph given starts at (-4, 0), goes through (-2, -2), (0, 0), (2, 2), and ends at (4, 0).
To determine where the graph is concave up, we need to find where the curvature of the graph is positive. This occurs when the second derivative of the function is greater than 0.
Based on the points provided, we can see that the graph is concave up between (-2, 2), as the curvature changes from negative to positive.
Therefore, the correct answer is: (-2, 2).
#1 ok
#2 4^x grows faster than any polynomial
#3 I think more likely (-4,0), as in
y = 2sin(pi/4 x)
http://www.wolframalpha.com/input/?i=2sin(pi%2F4+x)