Answer:
Rate of change of function [tex]h(x) = 2^x[/tex] on the interval [tex]2\leq x\leq 4[/tex] is; 6.
Step-by-step explanation:
Given the function: [tex]h(x) = 2^x[/tex] on the interval [tex]2\leq x\leq 4[/tex]
Rate of change of function: Let f be the function defined on the interval [tex]a\leq x\leq b[/tex], then the rate of change of function A(x) is given by:
A(x) = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
at x = 2;
h(2) = [tex]2^2= 4[/tex]
and at x = 4
h(4) = [tex]2^4= 16[/tex]
then, by the definition of rate of change of function:
A(x) = [tex]\frac{h(4)-h(2)}{4-2}[/tex]
Substitute the value of h(2) = 4 and h(4) = 16 we have;
[tex]A(x) = \frac{16-4}{4-2}=\frac{12}{2} = 6[/tex]
Therefore, the rate of change of function is 6.
