What kinds of optimization problems would be typical in graphics?

Why is it true that the gradient points in the direction of steepest ascent? I get the intuition behind it, but the justification seems non-obvious.

Is it common to use second order derivatives info for optimizations in computer graphics?

How is this used in graphics?

Is this heavily used in geology and geography graphics?

Would stochastic gradient ascent work better in many optimization tasks?

What kinds of optimization problems would be typical in graphics?

Why is it true that the gradient points in the direction of steepest ascent? I get the intuition behind it, but the justification seems non-obvious.

Is it common to use second order derivatives info for optimizations in computer graphics?

How is this used in graphics?

Is this heavily used in geology and geography graphics?

Would stochastic gradient ascent work better in many optimization tasks?