Question

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

Answer 1

Take derivitive of each

f'(x)=9
g'(x)=4
h'(x)=12x

so duh, when x>0.75 then h(x) grows at fastest rate, after that. it just keeps going up

Answer 2

Answer:

$\text{Exponential Function: }g(x)=4^x$

B is correct.  

Step-by-step explanation:

Given:  

$\text{Linear Function: }f(x)=9x+14$

$\text{Exponential Function: }g(x)=4^x$

$\text{Quadratic Function: }h(x)=6x^2+1$

All the functions are specific function.  

Growth rate of these function. ( If all are in same increasing )

Exponential > Quadratic > Linear  

For increasing value of x

All three functions are increasing function.  

Please see the attachment for graph for grow.

Hence, Exponential function grow fastest rate for increasing value of x is g(x)=4ˣ