For what value(s) of c will the following f(x) be differentiable?Please give an explanation for your answer.?

Question

c E R ie c is a real number

f(x) is defined in 3 parts.

f(x) = 4*(x^0.5) for x>0

f(x) = c for x=0

f(x) =4*(-x^0.5) for x<0

I personally think no value of c would work.I would be interested to hear your opinions especially how to differentiate f when x<0 .

Answer 1

There is no value of c that makes f(x) differentiable, but there is a value that makes it continuous.

As for x &lt; 0, I interpreted your equation as 4 * ((-x)^0.5)) which is clearly differentiable for x &lt; 0:

f&#039;(x) = -(4)(0.5)/((-x)^0.5) = -2/((-x)^0.5)

Another equation that would make sense would be:

f(x) = -4*((-x)^0.5) for x&lt;0