Question

MATH GENIUS NEEDED!!

Answer 1

So in calculus i learning about Derivatives and i need help with Diffrientiability.

Answer 2

Question 1: If possible, give an example of where a function is differentiable at a point but not continuous at that point.

Answer 3

not possible.
if a function is differentiable at a point it is also continuous at the point

Answer 4

please write a question

Answer 5

Indeed what he said, for a function to be differentiable at a point it must also be continuous at that point.

Answer 6

ty! Without a graph, how can one show differentiability of a function at a point?

Answer 7

By differentiating the function, and plugging in that point and checking it's valid.

Answer 8

GJ agent

Answer 9

Where is the function \[g(x) = 3x ^{2} - x +5\] differentiable?

Answer 10

so it is differentiable everywhere
no problems with any point and no points of discontinuities

Answer 11

okay.

Answer 12

Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.

Answer 13

well we can think of it as a slope.
you see that that slope right before x = 2 is infinity and right after is -infinity
so the slope of the graph at this point is not defined

Answer 14

oh. its an asymptote?

Answer 15

no, asymptote is different.
in our case its the slope value that goes to infinity and not the values of the function that goes to inf!

Answer 16

oh. Okay.

Answer 17

Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.

Answer 18

so the derivative at both sides of the point should be the same
we can see that if we come to the point from left
the derivative is negative
whereas when we come from the right it is positive

Answer 19

If a graph has ANY kind of corner like that, it is not differentiable at that point.

Smooth curves are differentiable. Corners are not.

If the slope suddenly changes, as it does in a corner = not differentiable