Which function grows at the fastest rate for increasing values of x? g(x)=14x f(x)=2x2−x h(x)=3x p(x)=12x3+9

Determine which function grows at the fastest rate for increasing.

In order to determine, we take the derivative of each function, then after that we solve for x.

Solution:

g(x) = 14x 

g'(x) = 14

x = 0

Since we do not have any other values that can be solve only a constant, then we'll have the value of 0 for x.

f(x) = 2x^2 -x

f'(x) = 4x - 1

Equate 4x -1 to 0 then transfer -1 on the other side of the equation, we must take note that when transposing a number, the sign changes.

4x - 1 =0

4x = 1

x = ¼

h(x) = 3x

h'(x) = 3

x = 0

Samce case as g(x)

p(x) = 12x^3 + 9

p'(x) = 36x^2 + 9

36x^2 = -9

x^2 = -9/36 or - ¼

We cannot take the square root of a negative number since the answer will be a complex number, or an imaginary number.

x = no solution

Final answer:

Based on the values, we have the function the has the fastest rate of change, and that is f(x) = 2x^2 -1