Application Of Derivatives For Class 12

Application of derivatives includes determining the rate of change of quantities, finding the equation of tangent and normal to a curve at a point, to find the turning points on the graph of a function occurs. etc.

Rate of change of quantity-

Consider a function y = f(x), the rate of change of a function is defined as-

\(\frac{dy}{dx} = f'(x)\)

Further, if two variables x and y are varying to another variable, say if x = f(t), and y = g(t), then using Chain Rule, we have:

\(\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}},\),

where \(\frac{dx}{dt} \neq 0\)

Application Of Derivatives For Class 12

Increasing and Decreasing Functions:

Consider a function f, continuous in [a,b] and differentiable on the open interval (a,b), then

(i) f is increasing in [a,b] if \(f'(x)>0\) for each \(x \in (a,b)\)

(ii) f is decreasing in [a,b] if \(f'(x)< 0\) for each \(x \in (a,b)\)

(iii) f is constant function in [a,b], if \(f'(x) = 0\) for each \(x \in (a,b)\)

Application Of Derivatives For Class 12
Application Of Derivatives For Class 12


Practise This Question

Let the complex numbers z1,zand z3 be the vertices of an equilateral triangle. Let z0 be the circumcentre of the triangle, then z21+z22+z23=