Let f(x)=x2+2x+3 . What is the average rate of change for the quadratic function from x=−2 to x = 5? Enter your answer in the box.

Question

asked Apr 5, 2018 101k views

2 Answers

Alphapage · Answer 1 · 2018-04-12T04:48:21+0000

Answer: 5

Explanation:

The average rate of change for the function f(x) from x=a to x=b is given by :-

(f(b)-f(a))/(b-a)

The given function :
f(x)=x^2+2x+3 (Its a quadratic function with degree 2.)

The average rate of change for the quadratic function from x=−2 to x = 5 will be :-

$(f(5)-f(-2))/(5-(-2))\\\\=(((5)^2+2(5)+3)-((-2)^2+2(-2)+3))/(5+2)$ [Note (-)(-)=(+)]

$=(25+10+3-(4-4+3))/(7)\\\\=(38-(3))/(7)\\\\=(35)/(7)=5$

Hence, the average rate of change for the quadratic function from x=−2 to x = 5 is 5 .