Applications of Derivatives in IB Mathematics

Applications of Derivatives in IB

Mathematics-

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   ({x_1},{y_1}), 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   ({x_1},{y_1})

m=  {\frac{{dy}}{{dx}}_{at({x_1},{y_1})}}

=f'({x_1})

Finally to find the equation of tangent we use the slope-point form of equation

y - {y_1} = m(x - {x_1})

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
i.e     {m_1} = {m_2}
(ii) If two lines are perpendicular to each other, the product of their  slopes is always -1

{m_1}.{m_2} = - 1

(iii) If a line is passing through two points   ({x_1},{y_1}) and  ({x_2},{y_2})  then, slope of the line

m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}

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