Discontinuity and Non Differentiability given a function f(x)

Question

Examine the function f(x)= (4(x+1)^2/5)/x^2-x-6 for points of discontinuity and non differentiability.

a) obtain a graph of the function on -8< or equal to x < or equal to 8 and -3 < or equal to y < or equal to 4.

b) examine the graph of this function. At what points is the function discontinuous? Give reasons

c) At what points is the function non-differentiable? Give reasons for your answers. Note: you may need to examine some "suspicious" points more closely by using a close-up graph or some slope tables.

Answer 1

I suspect that you mean f(x)= (4(x+1)^(2/5))/(x^2-x-6)

Note that (x+1)^2/5 means to raise x+1 to the 2nd power and then divide that result by 5. If want the power to be 2/5 you better pit it in parenthesis.

Why do you need a calculator? I am confused!

To find points of discontinuity you set the denominator top 0 and solve for x.

So solve x^2-x-6

Compute the derivative and see where it does not exist.

Throw away your calculator