Question

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

f(x)=4x2+9x
h(x)=2x
g(x)=18x

Answer 1

Answer choice should be B

Polynomial functions A and C are slow growers compared to the exponential function B

If you want to see this in action, make up a table of values. You'll see the y values for 2^x get very large and eventually need scientific notation

Hoped this help you buddy! :D

Answer 2

Answer with explanation:

The given functions in x are

1. f(x)=4 x² + 9 x

2. h(x)= 2 x

3. g(x)=18 x

To check whether the function is increasing or not , there are two ways

1. The graph of function is sloping Upwards.

2. For, two real x number ,that is if , a ≥ b, then , f(a) ≥ f(b).

All the three given function in x, are increasing because ,for increasing , x , value of function increases.

For Integral numbers,

⇒Function 1

f(x)=4 x² + 9 x

f(1)=4×1²+9×1

=4 +9

=13

f(2)=4×2²+9×2

=4 × 4 +18

=16 +18

= 34

f(2) - f(1)=34 - 13

= 21

→→Function B

h(x)= 2 x

h'(x)=2

Rate of change of function is constant, which is equal to 2.

→→Function C

g(x)=18 x

g'(x)=18

Rate of change of function is constant, which is equal to 18.

≡⇒→Rate of change of function ,f(x) is maximum among three functions.That is, f(x)=4 x² + 9 x , has highest rate of increasing, for increasing value of, x.