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?