What is differentiation of Secx?

What is differentiation of Secx?

sec x = sec x tan x. Proof. tan x = sec2 x. Proof. cot x = – csc2 x.

What does H mean in derivative formula?

The value of. f(a+h)−f(a)h. is the slope of the line through the points (a,f(a)) and (a+h,f(a+h)), the so called secant line.

Is the second derivative the slope of the first derivative?

The second derivative is acceleration or how fast velocity changes. Graphically, the first derivative gives the slope of the graph at a point. The second derivative tells whether the curve is concave up or concave down at that point.

What happens when the second derivative is 0?

3. The second derivative is zero (f (x) = 0): When the second derivative is zero, it corresponds to a possible inflection point. If the second derivative changes sign around the zero (from positive to negative, or negative to positive), then the point is an inflection point.

Can the second derivative test fail?

Inconclusive and conclusive cases The first derivative test can sometimes conclusively establish that a given critical point is not a point of local extremum. The second derivative test can never conclusively establish this. It can only conclusively establish affirmative results about local extrema.

Do points of inflection have to be differentiable?

Readers may check that are points of inflection. A point of inflexion of the curve y = f(x) must be continuous point but need not be differentiable there. Although f ‘(0) and f ”(0) are undefined, (0, 0) is still a point of inflection.

Can inflection points be Extrema?

3 Answers. It is certainly possible to have an inflection point that is also a (local) extreme: for example, take y(x)={x2if x≤0;x2/3if x≥0. Then y(x) has a global minimum at 0.Aban 18, 1390 AP

What do inflection points tell us?

Inflection points are points where the function changes concavity, i.e. from being “concave up” to being “concave down” or vice versa. They can be found by considering where the second derivative changes signs.

What is the derivative at an inflection point?

Inflection points are where the function changes concavity. Since concave up corresponds to a positive second derivative and concave down corresponds to a negative second derivative, then when the function changes from concave up to concave down (or vise versa) the second derivative must equal zero at that point.

How many inflection points are there?

If the slope is decreasing, the graph is concave down. So at each max or min point of f′(x) the slope changes from increasing to decreasing or the other way. Since there are 5 such place, that’s how many inflection points there are.Farvardin 2, 1398 AP