Is f(x)=(x^2-9x+14)/(x-7) differentiable at x=7?
stuck between these two choices:
a. No, b/c f'(x)=0 at x=7
v. No, b/c f(x) is not continuous at x=7

Question

Is f(x)=(x^2-9x+14)/(x-7) differentiable at x=7?
stuck between these two choices:
a. No, b/c f'(x)=0 at x=7
v. No, b/c f(x) is not continuous at x=7

zepdrix · Answer

The letters go all the way from A, to V? 0_o

jhannybean · Answer

Ask yourself whether 7 is even part of the domain of the function. Does your function have a non-vertical tangent line at $(7,f(7))$?

zepdrix · Answer

Differentiability implies Continuity

anonymous · Answer

v is suppose to be "b"

jhannybean · Answer

Like if the point theyre looking for lies on the domain of $f(x)$ then theres going to be a slope at that point

anonymous · Answer

I'm leaning towards b

zepdrix · Answer

hmm me too :) let's see what lady bean has to say about it though

jhannybean · Answer

You cant differentiate a function that has any sharp turns, breaks, etc that will make your function "non smooth"

jhannybean · Answer

Yeah, i agree b is the right choice.