Class 12 Maths Formula for chapter-6 Application of Derivatives
Math Formulas
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Application of Derivative
Increasing and Decreasing Functions
Let function f, continuous in [a,b] and differentiable on the open interval (a,b), then
- f is increasing in [a,b] if f'(x)>0 for each x in (a,b)
- f is decreasing in [a,b] if f'(x)< 0 for each x in (a,b)
- f is constant function in [a,b], if f'(x) = 0 for each x in (a,b)
Frequently Asked Question (FAQs)
Q1. What is the derivative formula?
Ans. Derivatives are a fundamental tool of calculus. A derivative of a function of a real variable measures the sensitivity to change of a quantity, which is determined by another quantity. Derivative Formula is given as, f _{1}( x ) = Lim△ x → 0 f ( x + △ x ) − f ( x ) △ x.
Q2. What are the applications of Derivatives?
Ans. Applications of Derivatives in Maths
- Finding Rate of Change of a Quantity.
- Finding the Approximation Value.
- Finding the equation of a Tangent and Normal To a Curve.
- Finding Maxima and Minima, and Point of Inflection.
- Determining Increasing and Decreasing Functions
Q3. What is Derivatives maths class 12?
Ans. The rate of change of a y concerning another x is called the derivative or differential coefficient of y with respect to x.
Q4. What is the limit formula?
Ans. Consider y = f (x) as the function of x. If in point x = a, f (x) takes an indefinite form, then we can consider the values of the function which is closest to a. If these values are inclined to a specific unique number as x tends to, that unique number is called the f (x) limit of x = a.
Q5. How do you solve derivation?
Ans. Following are the steps mentioned below:
- Divide both sides of the equation px^{2} + qx + r = 0 by p.
- Transpose the quantity c/a to the right side of the equation.
- Complete the square by adding b^{2} / 4a^{2} to both sides of the equation.
- Factor the left side and combine the right side.
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