Find k for Continuous f(x) & Differentiability at 2

In summary, the conversation discusses the continuity and differentiability of the function f(x) for different values of k. It is concluded that at k=3, f(x) is continuous and at k=4, it is differentiable. However, there is some disagreement on whether the derivative from the left and right at x=2 are equal, leading to a discussion on how to approach the problem.
  • #1
fiziksfun
78
0
OKKK,

f(x) =

2x + 1, for x =< (greater than or equal to) 2
.5x^2 + k for x > 2

---

FOR what value of k will f be continuous ?

MOST IMPORTANTLY, if k=4, is f differentiable at 2?
 
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  • #2
you're going to have to try a little harder than that
 
  • #3
why would you even respond if youre going to be rude?

i already did it i just wanted to see what other people got

at K = 3 it should be continuous and i think at k=4 it will be differentiable because the derivative from the left = 2 and the derivative from the right will be x or in this case 2

CORRECT? OR NOT?
 
  • #4
continuous for k=3.
because both functions have the same value @ x=2 and therefore the graph doesn't have a "jump" or a "step". More precisely, the limit @ x=2 (the transition point) is equal to some number.

for k=4, check at x=2.

if both equations are not equal then you cannot differentiate at that point.
 
  • #5
fiziksfun said:
why would you even respond if youre going to be rude?

i already did it i just wanted to see what other people got

at K = 3 it should be continuous and i think at k=4 it will be differentiable because the derivative from the left = 2 and the derivative from the right will be x or in this case 2

CORRECT? OR NOT?

i wasn't being rude because you're being ignorant. 1 this isn't the homework forum ,2 we don't do your homework for you, 3 i can't read your mind and know you've already done the problem.
 
  • #6
i am in calculus therefore i am ignorant!
 
  • #7
i really don't think that's the reason he thinks ur ignorant, its because u posted HW problems on the NOT-HW forum. THe calculus/analysis forum will tolerate help being asked for problems but generally not of this sort because it is somewhat formulaic. When I ask for help here I detail my solution (and i usually have a complete one at the time of posting). One typically asks for feedback on an idea they might have.
 

1. What is the definition of continuity for a function f(x)?

Continuity for a function f(x) at a point x=a means that the limit of f(x) as x approaches a exists and is equal to the value of f(a). In other words, the function does not have any jumps or breaks at that point.

2. How do you check for continuity at a specific point?

To check for continuity at a specific point, you need to evaluate the limit of the function as x approaches that point. If the limit exists and is equal to the function value at that point, then the function is continuous at that point.

3. What is the definition of differentiability for a function f(x)?

Differentiability for a function f(x) at a point x=a means that the derivative of the function exists at that point. In other words, the function is smooth and has a well-defined slope at that point.

4. How can you determine if a function is differentiable at a specific point?

You can determine if a function is differentiable at a specific point by checking if the limit of the difference quotient (the slope of the tangent line) exists as x approaches that point. If the limit exists, then the function is differentiable at that point.

5. What does it mean for a function to be continuous and differentiable at a point?

For a function to be continuous and differentiable at a point, it means that the function is both smooth and has no jumps or breaks at that point. This also means that the tangent line to the function at that point exists and is well-defined.

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