Question

for medal:
how do you find the derivative of g(x)= |2x+3|
those are absolute value signs.

Answer 1

power rule

Answer 2

is the answer just 2?

Answer 3

yeah

Answer 4

do the absolute value signs affect how you take the derivative?

Answer 5

why would they?

Answer 6

i don't know

Answer 7

do you know what abs signs mean?

Answer 8

no

Answer 9

what do they mean?

Answer 10

oh heck no

Answer 11

satellite, the answer is not 2?

Answer 12

no

Answer 13

why?

Answer 14

\[f(x) = |2x+3| = \left\{\begin{array}{rcc}
-2x-3& \text{if} & x < -\frac{3}{2} \\
2x+3& \text{if} & x \geq -\frac{3}{2}
\end{array}
\right.
\]

Answer 15

so your derivative is \[f'(x) = \left\{\begin{array}{rcc}
-2& \text{if} & x < -\frac{3}{2} \\
2& \text{if} & x > -\frac{3}{2}
\end{array}
\right.\]

Answer 16

and also it is not defined at \(x=-\frac{3}{2}\) since the limit does not exist there, i.e. since \(-2\neq 2\)

Answer 17

absolute value is a piecwise function, that is why, even though it seems easy when you first see it in grade school, it is a real pain in the arse later on

Answer 18

i'm looking at my textbook and it says that a critical number exists when the derivative=0 or when the derivative does not exist (like u said earlier).

Answer 19

thank you. it makes sense now.