Increasing and decreasing functions
This is my third post in the series of “Applications of derivatives”. The previous two were based on “Tangent and Normal” and “Maxima and Minima”.In this post, we shall learn about increasing and decreasing functions. That is one more application of derivatives.
Increasing and Decreasing Functions- We shall first learn about increasing functions
(a) Strictly increasing function- A function f (x) is said to be a strictly increasing function on (a, b) if x1< x2 f(x1) < f (x2) for all xl, x2(a, b).Thus, f(x) is strictly increasing on (a, b) if the values of f(x) increase with the increase in the values of x.Refer to the graph in below-given figure Read more
Applications of Derivatives in IB
In my previous post, we discussed how to find the derivative of different types of functions as well as the geometrical meaning of differentiation. Here we are discussing Applications of Derivatives in IB Mathematics
There are many different fields for the Applications of Derivatives. We shall discuss a few of them-
Slope and Equation of tangents to a curve- If We draw a tangent to a curve y=f(x) at a given point , then
The gradient of the curve at given point=the gradient of the tangent line at given point
and we already discussed that slope or gradient of the tangent at given point
Finally to find the equation of tangent we use the slope-point form of equation
The major part of this concept is also discussed in the previous post. We should also remember following points while solving these types of questions.
(i) If two lines are parallel to each other, their slopes are always equal
(ii) If two lines are perpendicular to each other, the product of their slopes is always -1
(iii) If a line is passing through two points and then, slope of the line