Question

4, find the -values (if any) at which is not
continuous. Which of the discontinuities are removable?

Answer 1

this function is a polynomial, and so it is continuous everywhere

Answer 2

how do i verify it?

Answer 3

oh im sorry i made a mistake, i put the wrong question

Answer 4

not sure what you mean
you have a quadratic polynomial
polynomials are always continuous

Answer 5

im so sorry this is the correct question

Answer 6

because you have a quadratic, the \(c\) you are supposed to find will be right in the middle of the interval, but we can work it out if you like

Answer 7

yes please

Answer 8

you need a couple numbers
what is \(f(3)\) ?

Answer 9

-1

Answer 10

ok and what is \(f(0)\) ?

Answer 11

8

Answer 12

right, so we need
\[\frac{f(b)-f(a)}{b-a}\] with \(a=0,b=3\) and we get \[\frac{f(3)-f(0)}{3-0}=\frac{-1-8}{3}=\frac{-9}{3}=-3\]

Answer 13

now we need the derivative of \(f(x)=x^2-6x+8\)
you got that one?

Answer 14

no

Answer 15

could you explain that?

Answer 16

by the power rule, if \(f(x)=x^2-6x+8\) then \(f'(x)=2x-6\)
does this look familiar?

Answer 17

a little

Answer 18

i recognize the power rule

Answer 19

not to be critical, but if you are having trouble taking the derivative of a polynomial then this question is way beyond that
in any case since we have
\[f'(x)=2x-6\] to find the \(c\) you are looking for, set
\[f'(c)=2c-6=-3\] and solve for \(c\)

Answer 20

c=3/2