Question

Determine for what numbers, if any, the given function is discontinuous. I will post pic

A. 5

B. None

C. 0

D. -5, 5

Answer 1

both pieces x-5 and x^2-10 on their own are continuous for every x

Answer 2

so the only possible point of discontinuity is at the junction of the two pieces

Answer 3

What is the value of x-5 when x = 5 ?

Answer 4

0

Answer 5

so C? @jim_thompson5910

Answer 6

yes, x-5 = 0 when x = 5

Answer 7

what about x^2 - 10 ?

What is the value of x^2 - 10 when x = 5?

Answer 8

15

Answer 9

So the y value of x-5 is 0, but the y value of x^2-10 is 15

If this piecewise function were continuous, then these two y outputs would be the same

Since they are not the same, the function is NOT continous

Answer 10

So the point of discontinuity is at x = 5

Answer 11

but if you use -5, you get
(-5)-5=-10
(-5)^2 -10=15

at -5 the y values are different
same goes for O

Answer 12

It might help if we actually graphed the two functions

Answer 13

One sec while I do that

Answer 14

Take a look at the attached for the graph

Answer 15

Notice how at the junction, there's a jump from the blue line to the red curve

Answer 16

hmm it looks different when i graph it on my calculator..

Answer 17

keep in mind the restrictions placed on each piece

Answer 18

oh yes! i totally forgot! so it is A. thanks!

Answer 19

1 more question please?

Answer 20

it is A, go for it

Answer 21

Find the slope of the tangent line to the graph of f at the given point.

f(x) = sqrt(x) at ( 36, 6)


A. 1/3

B. 12

C. 3

D. 1/12

Answer 22

Are you familiar with the derivative rules?

Answer 23

i know the formula

Answer 24

So what do you get when you take the derivative of f(x)?

Answer 25

is that right?