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The Mean Value Theorem : In this section we will discuss the Mean Value Theorem.
Before we going through the Mean Value Theorem we have to cover the following theorem.
Rolle's Theorem : Assume f ( x ) is a function which satisfies all of the following.
1. f ( x ) is continuous on the closed interval [a,b].
2. f ( x ) is differentiable on the open interval (a,b).
3. f ( a ) =f (b )
Then there is a number c such that a < c < b and f ′ (c ) = 0 . Or, in other terms f ( x ) contain a critical point in (a,b).
Formulas Now there are a couple of nice formulas which we will get useful in a couple of sections. Consider that these formulas are only true if starting at i = 1. You can, obv
Given f (x) = - x 2 + 6 x -11 determine each of the following. (a) f ( 2) (b) f ( -10) (c) f (t ) Solution (a) f ( 2) = - ( 2) 2 + 6(2) -11 = -3 (
Volumes of Solids of Revolution / Method of Rings In this section we will begin looking at the volume of solid of revolution. We have to first describe just what a solid of rev
how to Multiplying Rational Expressions ? To multiply fractions, or rational expressions, you must multiply the numerators and then multiply the denominators. Here's how it is
Linear Approximations In this section we will look at an application not of derivatives but of the tangent line to a function. Certainly, to get the tangent line we do have to
In a polygon no 3 diagnols are concurrent. If the total no of points of intersection are 70 ( interior ). find the no. of diagnols? Ans) Since no 3 diagonals are concurrent, There
integrate x over x+1
An unbiased die is tossed twice .Find the probability of getting a 4,5,6 on the first toss and a 1,2,3,4 on the second toss
Variable stars are ones whose brightness varies periodically. One of the most visible is R Leonis; its brightness is modelled by the function where t is measured in days.
The probability of a rare disease striking a described population is 0.003. A sample of 10000 was examined. Determine the expected no. suffering from the disease and thus find out
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