Question

Inverse functions and their derivatives

Answer 1

@freckles

Answer 2

have you solved f'(x)=0?

Answer 3

that is a quadratic equation

Answer 4

yes i got \[x = \sqrt{6 - x}\]

Answer 5

no no
that isn't how you solve for x
you need to get x on one side
you have x both sides

Answer 6

oh sould I use the quadriatic formula?

Answer 7

\[3x^2+3x-18=0 \\ \text{ my first step would be to divide by } 3 \text{ on both sides } \\ x^2+x-6=0\]
If you do not see that the left hand expression in the equation is factorable
you can choose to use the quadratic formula if you want...
I honestly like to factor when I can though

Answer 8

add six on each side then take out an x?

Answer 9

you cannot solve for x in that way

Answer 10

Oh wait I remember!!

Answer 11

(x+3)(x-2)

Answer 12

good job

Answer 13

\[(x+3)(x-2)=0 \implies x+3=0 \text{ or } x-2=0\]

Answer 14

so -3 and 2

Answer 15

yes

Answer 16

I will draw a numberline with -3 and 2 on it ...

Answer 17

now we know y=3x^2+3x-18 is a parabola so we know that this function looks like this U or and upside down U
since the number in front of x^2 is positive then we have the U

this is a rough graph of f'