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Is critical point also an inflection point?
no, a critial point is where the slope (or the derivitive) is 0. the inflection point is when the graph switches from concave up to concave down or vice versa
Why do you need to find the inflection point on a graph?
To find the inflection points on a graph, you need to take the second derivative. Then, set that equal to zero to find the x value(s) of the inflection point(s).
What you call the point when a curve changing from concave upward to concave downward?
The point when a curve changes from concave upward to concave downward is called the inflection point. It is the point where the curve transitions from being curved "upwards" to being curved "downwards" or vice versa. At the inflection point, the rate of change of the curve's curvature changes sign.
Is it always true that for any polynomial px if x is a zero of the derivative then x px is a maximum or minimum value of px?
No. The important decider is the second derivative of the polynomial (the gradient of the gradient of the polynomial) at the zero of the first derivative: If less than zero, then the point is a maximum If more than zero, then the point in a minimum If equal to zero, then the point is a point of inflection. Consider the polynomial f(x) = x3, then f'(x) = 3x2 f'(0) = 0 -> x = 0 could be a maximum, minimum or point of inflection. f''(x) = 6x f''(0) = 0 -> x = 0 is a point of inflection Points of inflection do not necessarily have a zero gradient, unlike maxima and minima which must. Points of inflection are the zeros of the second derivative of the polynomial.
What is a point of explosion in calculus?
I don't think such a term is used in calculus. Check the spelling. Perhaps you mean point of inflection?
