Let f(x) = (ax if x ≤ 1),

= (bx2+ x + 1 if x > 1)

(a) Find all choices of a and b such that f is continuous at x = 1.(b) Find values of a and b such that f is differentiable at x = 1.

(b) Draw the graph of f when a = 1 and b = -1.

(c)Find values of a and b such that f is differentiable at x=1.

(d) Draw the graph of f for the values of a and b found in part c.

If it is not possible to draw the graph, if you can tell me how to plot the points that would be very helpful for parts b and d.

I will greatly appreciate your help and thanks in advance.