Is this piecewise function differentiable at x =1

f(x) = {3x^2, if x<= 1}
f(x) = { 2x^3 + 1, if x > 1}

? 10 points.

OK Helium---- I'd say that the function is differentiable at x = 1. The function is continuous and defined at all x.
for x <= 1 f'(x) = 6x and = 6 at x = 1
for x> 1 f'(x) = 6x^2 and = 6 at x= 1.

Yes, if the slopes of the two pieces are the same at x = 1. No, if they are not.

The slope of the 3x^2 piece is 6x. At x = 1, that's a slope of 6,
What is the derivative of 2x^3 + 1? What is it at x = 1? Is it equal to 6?