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

[fiziksfun]

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?

 

[ice109]

you're going to have to try a little harder than that

 

[fiziksfun]

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?

 

[bob1182006]

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.

 

[ice109]

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.

 

[fiziksfun]

i am in calculus therefore i am ignorant!

 

[SiddharthM]

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.