Question

average rate of change for f(x) x=4 to x=7?

Answer 1

i think you forgot f(x)

Answer 2

its a whole assignment so i dont know what to do like i converted f(x) to a vertex form then into standard but i dont know

Answer 3

rate of change is the slope (Y2 -y1)/(x2 - x1 )
this is also the derivative depends on what class you are in dy/dx

Answer 4

f(x) = 2 (x - 6)^2 + 3 is f(x) in vertex i think

Answer 5

then i got y = 2x^2 - 24x - 69 for standard form

Answer 6

avg rate of chage = \[\frac{f(7)-f(4)}{7-4} \]

Answer 7

but then wouldnt that just be the same thing on top and bottom? f(3) / 3?

Answer 8

\(f(7)-f(4)\ne f(7-4)\)

Answer 9

and \(f(7)\ne 7\)

Answer 10

im so confused

Answer 11

If f(x) = 2 (x - 6)^2 + 3
How do you evaluate f(7) ?

Answer 12

2( 7 - 6)^2 + 3 ?

Answer 13

yes

Answer 14

do the same with f(4),

Answer 15

and then divide ?

Answer 16

well subtract those two results, and then divide by (7-4)

The idea here is that the rate of change is basically taking two points on your parabola, and then drawing a line through those points. Then the average rate of change is basically the slope of that lie you drew. Now, the slope of a line can be expressed as \[\frac{y_2-y_1}{x_2-x_1} \] , and remember you can write \(y=f(x)\), so that the formula becomes \[ \frac{f(x_2)-f(x_1)}{x_2-x_1}\]

Answer 17

for f(4) i got 19 and for f(7) i got 7

Answer 18

so i divide 19 and 7 by 3?

Answer 19

hm not quite :S I'm not sure how you calculated that. Remember the rules for exponents and parenthesis: Parenthesis first, then exponents, then multiplication/division, then addition/subtraction

Answer 20

2 (4-6)^2 + 3
2 (-2)^2 +3
-4 ^2 +3
16 + 3 = 19

Answer 21

2 (7-6) ^2 + 3
2 (1)^2 +3
2^2 + 3
4 + 3 = 7

Answer 22

2 (-2)^2 +3
this becomes 2(4)+3 since (-2)^2= 4 and it's an exponent, so you do it before the multiplication

Answer 23

11?

Answer 24

so 11 and 19?

Answer 25

2 (4-6)^2 + 3 = 11
--------------------------
2(7 - 6)^2 + 3
2(1)^2 + 3
2(1)+3
=5

Answer 26

oh i see both of my mistkes.. then what do we do with 11 and 5?

Answer 27

so from the formula \[\frac{f(7)-f(4)}{7-4}=\frac{5-11}{7-4}=\frac{-6}{3}=-2 \]

Answer 28

thank you so much! i was so lost before i wanted to break windows in my house

Answer 29

so average rate of change is -2?

Answer 30

yup

Answer 31

yw :), lol don't break any windows!