Respuesta :
The function p(x) is growing at the fastest rate for increasing the values of x.
What is the growth rate of the function?
The growth rate of any function f(x) means how fast the value of f(x) increasing or decreasing as the value of x increase.
According to the given question.
We have four functions.
[tex]g(x) = 14x[/tex]
[tex]p(x) = 12x^{3} + 9[/tex]
[tex]f(x) = 2x^{2} -x[/tex]
[tex]h(x) = 3x[/tex]
Now for finding the fastest growth rate of the function for increasing the values of x, we will simply put different values of x in the given four different functions.
For, x = 1
[tex]g(x)=1\\p(x) = 12(1)^{3} + 9 = 21\\f(x) = 2(1)^{2}-1= 1\\ h(x) = 3[/tex]
Similarly,
For x = 2
[tex]g(x) = 14(2) = 28\\p(x) = 12(2)^{3}+9 = 105\\ f(x) = 2(2^{2})-2=8-2 = 6\\ h(x) = 3(2) =6[/tex]
Hence, the function p(x) is growing at the fastest rate for increasing the values of x.
Find out more information about growth rate of the function here:
https://brainly.com/question/17179999
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