MATH SOLVE

4 months ago

Q:
# Find the Rate of Change of the function h(x)=2^x on the interval 2 β€ x β€ 4.

Accepted Solution

A:

Answer:Rate of change of function Β [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 = 4h(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.