Step 3:
Since both the condition are satisfied, Mean Value Theorem is applicable. \ There exist c (4, 10) such that \ f (4) = 0 f '(c) = 3c 2 - 36c + 104 Substituting these values in (1), we have ..
Since both the condition are satisfied, Mean Value Theorem is applicable. \ There exist c (4, 10) such that \ f (4) = 0 f '(c) = 3c 2 - 36c + 104 Substituting these values in (1), we have ..Example 3:
Differentiate y = (x+2) (x+3) by using the formul..
Differentiate y = (x+2) (x+3) by using the formul..Note 3:
d y and dy are not usually the same and dy is the approximate value of d y..
d y and dy are not usually the same and dy is the approximate value of d y..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 and f "(a) = 0. In this case we..
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 and f "(a) = 0. In this case we..Definite Integral as a Limit of Sum
Let f (x) be a single valued continuous function defined in the interval [a,b] where b > 0 and let the interval [a,b] be divided into n equal parts each of length h, so that nh = b - a; then we define ..
Let f (x) be a single valued continuous function defined in the interval [a,b] where b > 0 and let the interval [a,b] be divided into n equal parts each of length h, so that nh = b - a; then we define ..Rolle's Theorem
Let f be a real valued function in [a,b] such that f is continuous in [a,b]. f is differentiable in (a,b..
Let f be a real valued function in [a,b] such that f is continuous in [a,b]. f is differentiable in (a,b..Rolle's Theorem and Mean Value Theorem Rolle's Theorem - Let f be a real valued function in [a,b] such that f is continuous in [a,b]. f is differentiable in (a,b..
Rolle's Theorem - Let f be a real valued function in [a,b] such that f is continuous in [a,b]. f is differentiable in (a,b..Langrange's Mean Value Theorem
Let f be real valued function in [a,b] such that, 1. f is continuous in [a,b]. 2. f is differentiable in (a,b). ..
Let f be real valued function in [a,b] such that, 1. f is continuous in [a,b]. 2. f is differentiable in (a,b). ..See what our Users say :
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