application of derivatives in geometry

The word 'geometry' is derived from the Greek words 'geo' meaning 'earth' and 'metron', meaning 'measuring'. Geometry originated when man felt the need to measure his land. Ancient Egyptians were perhaps the first people to study geometry. Later, th..

Question: Give a definition for a) parallel lines b) perpendicular lines Are these other terms that need to be defined first? Answer: a) Given any straight line and a point not on it, there exists one and only one line which passes through that point and never intersects the given line..

Consider the statement of a theorem "If a transversal intersects two parallel lines, then pairs of corresponding angles are equal”. This theorem has two parts. If (hypothesis) and then (conclusion). Let us interchange the hypothesis and conclusion and write the statement. "If a..

Differential calculus can be considered as mathematics of motion, growth and change where there is a motion, growth, change. Whenever there is variable forces producing acceleration, differential calculus is the right mathematics to apply. Application of derivatives are us..

Conclusion - In this chapter we have learnt the application of derivatives to rate measure, also we have used the geometrical measurement of to find the equations of the tangent and normal to a curve at any point on the curve, angle of intersection of the curves. The deriva..

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x = a is called a point of inflexion. Rolle's theorem: If a function f(x) is such that (i) f (x) is continuous on [a,b] (ii) f (x) is differentiable on (a,b) and (iii) f (a) = f (b) Geometrical interpretation of Rolle's theorem Let AB be the graph of y = f(x) such that A = (a , f(a)) and B = (b , f..

The following results can be deduced from velocity-time graph. The acceleration produced in a body The distance covered by a moving object We can derive the equations of motion Let us see how to calculate the distance covered by a moving object from speed-time graph. The figur..

Trigonometry - is that branch of mathematics which deals with the measurement of sides and angles of triangles. The word, trigonometry is derived from Greek, which means the measure of triangles. This subject was originally developed to solve problems in astronomy and geometry. ..

Derivatives are also used to trace the graphs of different functions. To optimise the value of a differentiable function of practical use, derivatives of the functions are applied. This chapter reveals with many more application of derivatives such as determ..