Let f (x) be a function defined for all x, with −5 ≤ f (x) ≤ 10. Also, lim f(x) as x ->0 does not exist but f (0) = 3.

(a) Let g (x) = xf(x). Show g is continuous at x = 0.

i know that for the above i have to use the 3 conditions

f(c) exists

lim f(x) as x->0- = lim f(x) as x -> 0+

lim f(x) as x -> 0 = f(c)

(b) Does the graph of g have a tangent line at (0, 0)? Explain.

for this one i'm not sure because g(x)= xf(x)

so g'(x) = f(x) + xf'(x)

g'(x) = 3 + 0 * f'(x) [ i'm not sure about the value of f'(x)

can anyone help me with the value of f'(x) and whether g(0) has a tangent line