Question

I will FAN.
Please help with this calculus question.

Answer 1

for differentiability Lf'(x)=Rf'(x)

Answer 2

Here Lf'(3)=2.3=6 and Rf'(3)=m so we must have ,m=6

Answer 3

Where does LF come from?

Answer 4

Lf'(x) means the left hand derivative of f at the point x

Answer 5

and Rf'(x) means the right hand derivative of f at the point x

Answer 6

so for mx+b you would plug in 3 for x

Answer 7

no....

Answer 8

Wait... yeh ignore that. Sorry. Im super confused.

Answer 9

when x<=3, f(x)=x^2 and f'(x)=2x

Answer 10

when x>3, f(x)=mx+b and f'(x)=m

Answer 11

right??

Answer 12

Oh the derivatives of each. Okay i see now. right,

Answer 13

Lf'(3)=2.3=6 and Rf'(3)=m so both these must be equal for the function to be differentiable at x=3, so 6=m

Answer 14

and here b can take any real value. it has no restriction

Answer 15

Okay I understand that now, except for the b. Finding b. How is it any real value if its being added to m. and m is 6.

Answer 16

the differentiability has no relation with b here.. since f'(x) doesnot contain any thing related to b. so b can be any value,

Answer 17

@arianna1453

Answer 18

Okay. I think I have to find an actual value of b.

Answer 19

there will be no actual value. you take any place and place it for instance

Answer 20

oh wait a bit i think i have the answer

Answer 21

@arianna1453

Answer 22

see the function will be differentiable, so it will be continuous as well

Answer 23

now since we know the value of m, let us re-write the function

Answer 24

6x+b but b=-9 so its 6x-9 when x >3

Answer 25

f(x)=x^2,x<=3 f(x)=6x+b,x>3
now the left hand limits at x=3 is 3^2=9 and the right hand limit at x=3 is 18+b
so 9=18+b so b=-9

Answer 26

And x^2 and 6x-9 connect together when graphing.

Answer 27

Good, we both got it now. ahaha.

Answer 28

hence we have m=6,b=-9

Answer 29

Right. Agreed