Question

Calculus help

Answer 1

do u knw how to sketch the graphs seperatley without any restrictions

Answer 2

do u have a problem with sketching or showing continuity and differetntiability

Answer 3

i'm not good with graphs at all

Answer 4

I know that if a point doesn't lay on the line it's a discontinuity there

Answer 5

Let's focus on what you ARE good at.
Please try your hand at sketching the curve f(x) = x^2 + 4x + 2. Hint: the graph is a parabola which opens upward.
Please also sketch the curve of g(x) = -x^2 - 4x +1. Hint: parabola which opens downward.
Once you've done this, others and I would be better able to step in and help you further.

Answer 6

Ok thanks.

Answer 7

http://media.tumblr.com/tumblr_mcybkiUN1P1qcvqjt.jpg

Answer 8

(a) It is continuous.. I think?
(b) idek lol

Answer 9

@SolomonZelman

Answer 10

Lena: nice graphs! We want to know whether the function defined in this homework problem is continuous at x = -2. Please go back to your drawing and draw a vertical line thru x = -2. Do your two curves meet at x = -2, or disagree in y-value?
For continuity at x = -2, the two curves MUST meet/touch at x = -2. What's your conclusion?

Answer 11

one sec doing that now

Answer 12

There's two different points...

Answer 13

The question about differentiability of f(x) at x = -2 is a bit more abstract. I'd suggest you look up "differentiability" in your textbook or on the Internet. My university-level calculus textbook states that a discontinuity at a certain x value (such as x = -2 in your math problem) means that the function is not differentiable there. Interestingly enough, both of those two curves you graphed have derivatives equal to zero at x = -2, but really, we have TWO instead of ONE tangent line at x = -2. No soap. Not differentiable at x = -2.

Answer 14

Because you have "two different points" (on two different curves) when x equals or is very near to -2, you definitely have a discontinuity in the piecewise defined function f(x) of this math problem.

Answer 15

ok