Question

Identify intervals on which the function is increasing, decreasing, or constant.

g(x) = 4 - (x - 6)^2

Answer 1

help meee

Answer 2

@RadEn can you help me??

Answer 3

is it calculus ?

Answer 4

precalc!

Answer 5

have u learned about differential ?

Answer 6

a. Increasing: x < 4; decreasing: x > 4

b. Increasing: x < 6; decreasing: x > 6

c. Increasing: x < -6; decreasing: x > -6

d. Increasing: x > 4; decreasing: x < 4

Answer 7

not suree

Answer 8

use differential, take the first derivative of g(x)
so, if g(x) = 4 - (x - 6)^2 then g ' (x) = ...

Answer 9

hint : use the chain rule

Answer 10

can u ?

Answer 11

umm not sure how to do it...

Answer 12

well, to get g'
the other way is we simply the g(x), first
g(x) = 4 - (x - 6)^2 = 4 - (x^2 - 12x + 36) = -x^2 + 12x - 32

Answer 13

so, if g(x) = -x^2 + 12x - 32 then
g' = -2x + 12, right ?

Answer 14

yes!

Answer 15

now, g(x) would increasing when g' > 0 and decreasing when g'(x) < 0

Answer 16

case I :
g'(x) > 0
-2x + 12 > 0
-2x > -12
x < 6
this, intervals when g(x) would increas

Answer 17

case II :
g'(x) < 0
-2x + 12 < 0
-2x < -12
x > 6
this, intervals when g(x) would decreas

Answer 18

ohh so that makes the answer B right? Increasing: x < 6; decreasing: x > 6

Answer 19

yes

Answer 20

ahh i get it thank you!!!!!!:)

Answer 21

you're welcome