What is the basic idea for finding critical point via Morse theory and critical groups?

What is the Mixed Derivative Theorem for mixed second-order partial derivatives? How can it help in calculating partial derivatives of second and higher orders?

How do I find the y-intercept of a parabola?

What are the vertices of ${\displaystyle 9x^2+16y^2=144}$?

How to determine the rate of change of a function?

Why are the tangents for 90 and 270 degrees undefined?

How to find the center and radius of the circle ${\displaystyle x^2+y^2-6x+8y=0}$?

What is multiplicative inverse of a number?

How to find the continuity of a function on a closed interval?

How do I find the tangent line of a function?

How to find vertical asymptotes using limits?

How to find the center and radius of the circle ${\displaystyle x^2-12x+y^2+4y+15=0}$?

Let f be a function so that (below). Which must be true?
I. f is continuous at x=2
II. f is differentiable at x=2
III. The derivative of f is continuous at x=2
(A) I (B) II (C) I and II (D) I and III (E) II and III

How to find the center and radius of the circle given ${\displaystyle x^2+y^2+8x-6y=0}$?

How to find the center and radius of the circle ${\displaystyle x^2+y^2+4x-8y+4=0}$?

How to identify the center and radius of the circle ${\displaystyle {(x+3)}^2+{(y-8)}^2=16}$?