1. Well, I don't know that formula, but this is what I do.

The gradient at any point on a curve is given by the derivative of the curve.

Now, the gradient is 76. So, the derivative equals 76.

Now, plug in the value of x in the equation of the original curve.

2. Convert the upper fraction into one single fraction.

Try out part b now.

3. To get the x coordinates of the critical poinst, set the derivative (f'(x) not f(x) as in your post. I think this was a typo) to 0 and solve for x.

Then, if it is like the cube function, is there a maximum? A minimum perhaps? Or neither?