Question

Derivs
http://gyazo.com/da79c8768e1e4ff28a282298e1a5d458

Answer 1

Oh darn! I've done these before but I forgot D:

Answer 2

I know that m=6 by finding the deriv and inputting 1

Answer 3

3x^2, bring down 2, subtract 1, deriv=6x

Answer 4

6*1=6=m

Answer 5

y=mx+b, y=6x+b

Answer 6

So how to find b..

Answer 7

@jim_thompson5910

Answer 8

what is f(1)

Answer 9

Oh god, the one & only Jim thompson is here :D

Answer 10

;-;

Answer 11

6

Answer 12

you sure?

Answer 13

? How would it not be?:O

Answer 14

WAIT ITS 3

Answer 15

f(x) = 3x^2 when x >= 1

so f(1) = ???

Answer 16

good

Answer 17

I was using the deriv. to find it, not the original equation

Answer 18

so this means that the point (1,3) is on the function

Answer 19

for the function to be differentiable, it must be continuous

Answer 20

so what does that mean?

Answer 21

So now using the deriv for f'(1), y=6x+b, input (1,3) into it and solve for b?

Answer 22

for it to be continuous, the piece mx+b must be equal to 3 when x = 1, ie

y = mx+b

3 = m(1) + b

3 = m + b

in addition, when a function is differentiable, the slopes of the tangent lines of the function all exist and the slopes themselves make up a continuous function

what this means is that for this to be possible, the slope m must be 6 since you've shown that the slope of the tangent line at x = 1 is 6 (when you used the derivative of f(x) = 3x^2)

so m = 6 and you use this and 3 = m + b to find b

Answer 23

So then 3=6*1+b, 3=6+b
b=-3?

Answer 24

YES ITS RIGHT I LOVE YOU JIM

Answer 25

very good, so m = 6, b = -3 making your first piece to be 6x - 3