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.
