Question

Consider the function p(x) = x^2 + 6x + 5.
what is the average rate of change from x=1 to x=5

Answer 1

The average rate of change is 12.

Explanation:

Given

p(x)= x^2+6x+5

The average rate of change in the given interval a ≤ x ≤ b is given by the expression

Rate of change= (p(b)-p(a))/(b-a)

Here p(b) is the value of function at point b and p(a) is the value of function point a.

From the question,

a = 1

and

b = 5

So,

Rate of change= (p(5)-p(1))/(5-1)

Now,

p(5)= (5)^2+6(5)+5

p(5)=25+30+5

p(5)=60

And

p(1)= (1)^2+6(1)+5

p(1)=1+6+5

p(1)=12

Putting in the formula

Rate of change= (60-12)/(5-1)

= 48/4

=12