Question

Which function grows at the fastest rate for increasing values of x?

p(x)=5x3+3
f(x)=8x2−3x
h(x)=2x
g(x)=19x

Answer 1

Calculate the derivative of each function
And btw answer is p(x)

Answer 2

The function which has the fastest rate for increasing values of x are:

`p(x)=5x^3+3`

Explanation:

We are given four polynomial functions as:

`p(x)=5x^3+3\\\\\\ f(x)=8x^2-3x\\\\\\h(x)=2x\\\\\\g(x)=19x`

Now as we know that if the degree of the polynomial increases the function becomes more extreme i.e. it increases very quickly with the increasing value of x.

Hence, among the given options the function which has the fastest rate of increase is:

`p(x)=5x^3+3`

( Since, it's degree is 3 which is highest as compared to the other polynomials (one of degree 2 and 2 of degree 1) )