Question

determine the value of a so that the average rate of change of the function j(x)=3x²+ax-4 over the interval -1≤x≤2 is 8

Answer 1

did you try to set up the equation ?

Answer 2

i plugged the values of x into the equation and got two new equations if thats what you mean?

Answer 3

i got
f(2) = 10+ax
f(-1)= 1+ax
... ?

Answer 4

the equation is ( j(2) - j(-1))/(2 - -1) = 8

Answer 5

"average rate of change"
Perhaps the "slope" between the endpoints?

Answer 6

oh so i would just do ((10+ax)-(1+ax))/(2-(-1)) = 8?

Answer 7

except j(2) should not have any x's in it (because x is replaced by 2)
ditto for j(-1)

so redo that part

Answer 8

Oh wait ... so j(2) = 10+2a
j(-1) = 1-1a ?

Answer 9

yes

Answer 10

and then what i said earlier right?

Answer 11

though j(-1) is -1 - 1a , right ?

Answer 12

\[\frac{ (10+2a)-(-1-1a) }{ 2-(-1) }\] right?

Answer 13

wait... i think i did that wrong

Answer 14

and j(2) with j(x)=3x²+ax-4
is 3*4 + 4a -4 = 12 +4a -4 = 4a+8

Answer 15

\[\frac{ (10+2a)-(1-1a) }{ 2-(-1) }\]

Answer 16

doesnt x=2 not 4?

Answer 17

oops j(2) is
and j(2) with j(x)=3x²+ax-4
is 3*2*2 + 2a -4 = 12 +2a -4 = 2a+8

Answer 18

OH WOW!! IVE BEEN PUTTING 2 INSTEAD OF 4 for the end number

Answer 19

and j(-1) is
3*-1*-1 + -1*a -4 = 3 -a -4 = -a - 1

Answer 20

\[\frac{ 8+2a-(-1-a) }{ 2-(-1) }\]

Answer 21

yes and that is equal to 8 (the average rate of change)

Answer 22

soooooo \[\frac{ 9+3a }{ 3 }\]\[3+a\]\[a=8-3\]\[a=5\]

Answer 23

yay ! thaankkkss @phi

Answer 24

yw