Differentiation

[rosey1012]

I don't understand how to complete this question:

f(x) = x^2 + 4x + 7 if x ? 2
= ax + b if x > 2
differentiable at 2

(a) It is known that if a function is differentiable at a point
c, then it is continuous at c. Using now the continuity of f at
2, we can establish a relationship between a and b. Find this
relationship and express it in the form b = Aa + B, where A and
B are constants.
Answer: b=____a+____

(b) Assuming that x>2, one can simplify the quotient

(f(x)-f(2))/(x-(2))

into the form Ca + D, where C and D are constants. Find
these constants.

Answer: C=____ and D=_____

Hint. Don’t forget that you can use the result from part (a) to eliminate b from the expression

(c) Assuming that x<2, one can simplify the quotient

(f(x)-f(2))/(x-(2))

into the form Ex+F, where E and F are constants. Find these constants.

Answer: E=____ and F=_____

(d) Using the results of parts (a), (b) and (c), ?nd the values
of a and b.

Answer: A=____ and B=____

 

[tkhunny]

You can't do ANY of it?

A limit exists if the one-sided limits exist and are equal. You must use this to do the first part.

Let's see what you get and we can talk about the rest.

 

[rosey1012]

i understand part a and d, the only parts i don't understand are b and c

 

[tkhunny]

Please demonstrate. Seriously, show your work or your post just looks like you're trying to get someone else to do your homework.

For b, think on the definitions of a derivative. This should look familiar.