The percentage of points scored by Jack each year during his four year..
The percentage of points scored by Jack each year during his four year degree course is shown in the table. Which is the equivalent box-and-whisker plot for the data? Also find the average percentage of points scored by him during the course. Year Percentage of points ..
Interpretation of Derivative at a Point
Physical Significance: Let Q (t) be a quantity that changes with time 't'. Let D t be the increment given to 't' and D Q be the corresponding increment in Q, then is called the average rate of change of Q with respect to 't'. (Also known as Newton - quotient of f at t..
Physical Significance: Let Q (t) be a quantity that changes with time 't'. Let D t be the increment given to 't' and D Q be the corresponding increment in Q, then is called the average rate of change of Q with respect to 't'. (Also known as Newton - quotient of f at t..Derivative of a Function
Derivative of a Function - So far we have discussed the derivative of a function f(x) at a point 'a' which is in the domain of f. Suppose we want to find the derivative of the same function at a different point 'b', then we have to compute the ..
Application of Derivatives
Conclusion - In this chapter we have learnt the application of derivatives to rate measure, also we have used the geometrical measurement of dy/dx to find the equations of the tangent and normal to a curve at any point on the curve, angle of intersection of the curve..
Right Hand Derivative
Let f be a function of x (y=f(x)). Let a be a point in the domain of f. The RHD of f at a is defined as where h>0, provided the limit exist..
Let f be a function of x (y=f(x)). Let a be a point in the domain of f. The RHD of f at a is defined as where h>0, provided the limit exist..Theorem 3: (Second Derivative Test)
Let f be a differentiable function on an interval I and let a I. Let f "(a) be continuous at a. Then i) 'a' is a point of local maxima if f '(a) = 0 and f "(a) < 0 ii) 'a' is a point of local minima if f '(a) = 0 and f "(a) > 0 iii) The test fails if f '(a) = 0 a..
Let f be a differentiable function on an interval I and let a I. Let f "(a) be continuous at a. Then i) 'a' is a point of local maxima if f '(a) = 0 and f "(a) < 0 ii) 'a' is a point of local minima if f '(a) = 0 and f "(a) > 0 iii) The test fails if f '(a) = 0 a..Points to Remember
Modes of reproduction in plants can be grouped into 2 types a) asexual b) sexual reproduction Regeneration of new plants from portions of vegetative organs is very common. Runner, rhizome, bulbs, corns and tubers serve as means of propagation. A population of genetically identi..
Find the point of inflection of f(x) = x3 - 12x2 + 197.
Find the point of inflection of f ( x ) = x 3 - 12 x 2 + 197. => (- 4, -59) or (4, 69) or (12, 197) or (0, 197)..
Find the points of inflection for f(t) = t4 - 8t3 + 10.
Find the points of inflection for f ( t ) = t 4 - 8 t 3 + 10. => (0, - 10) and (- 4, - 246) or (0, - 10) and (4, 246) or (0, - 10) and (4, - 246) or (0, 10) and (4, - 246) or (0, 10) and (- 4, 246)..
Result
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