What is second derivative?

Question

First derivative of a function means a tangent to that point of the function.What does the second derivative means practically on the graph of that function?

Answer 1

if the second derivative is >0 the graph is concave up at that point
if the second derivative is <0 the graph is concave down at that pt
if the second derivative is =0 the there is an inflection point on the graph there.

Hope that helps!

Answer 2

first derivative is just the instantaneous slope, i.e. the instantaneous rate of change. Which is the same as the slope of a tangent to the curve (but not "the tangent" itself). in physics, the first derivative of the position, with respect to time, is the speed - the speed is the rate of change in the position, with respect to time.

second derivative is the rate of change of the slope. In physics, the rate of change in the speed, is called the acceleration. On a graph, when the 2nd derivative is positive it means that the 1st derivative is increasing all the time, so you've got a graph that is concave upwards. And if negative, concave downwards.

hope this helps

Answer 3

Plot first derivatives of all points in a graph. Now, draw tangents to each of this derivative function again. What we have found now is second derivative. Likewise we can go on differentiate the functions till it vanish thereby getting higher order differentials.

Answer 4

if you plot a function f(x) against x, and draw a tangent at any point (x,f(x)), first derivative i.e. f'(x) at that point will indicate the value of slope at that particular point.

now, u find different values of f'(x) for different x which means f'(x) is also dependent on x and undergo a regular change depending on the manner of the function. if you plot f'(x) against x u'll find a curve. draw a tangent at any point (x,f'(x)). now, second derivative f"(x) will show the result of the slope again.

additionally, if f"(x)<0, f(x) at point x has a highest peak
if f"(x)>0, f(x) at point x has a lowest peak
if f"(x)=0, f'(x) at point x has a highest/lowest value.

the reasons can be explained but with additional graphs and figures its difficult to explain.

Answer 5

Second derivative is the turning points, for function f, f' is the change in f (the tangent of f) so f'' is the change in the tangent of f.

Answer 6

I seem to remember that it indicates wether or not the point on the graph is an increasing curve, a decreasing curve or a stationary point. If the 2nd derivative is less than 0 then the curve is increasing, if it equal to 0 then it is a maximum point, a minimum point or point of inflexion or if it more than 0 then the curve is decreasing. This is all from memory, you might want to check other peoples answers too.

Answer 7

The derivative of a derivative (known as the second derivative) describes the rate of change of the rate of change, and can be thought of physically as acceleration.

Answer 8

first derivative is the rate, speed or velocity

while second derivative is the derivative of the derivative
it is the velocity of the velocity

or simply the ACCELERATION

Answer 9

well second derivative means that its the rate of change of slope of the function.
it tells wheter the function shall concave or convex in nature while increasing or decreasing
1.if second derivative is + : function shall be convex
2.if second derivative is -:function graph at that piont is concave.
it tells wheter a function is increasing in decreasing or increasing way or vice versa.

Answer 10

it is the measure of the curvature at that point.