f x x 1 x 2 x 3 in 0 4 Mathematics Question Verify Lagrange s mean value theorem for the function f x x 1 x 2 x 3 in interval 0 4 and also find out the value of C Solution Verified by Toppr f x x 1 x 2 x 3 0 4 According to Lagrange s mean value theorem f o 1 2 3 f o f b f a b a f 4 3 2 1 6 6 4 0
Verified by Toppr Correct option is C 2 pm dfrac 2 sqrt3 3 textbf Step 1 Differentiate the given polynomial function text We have f x x 1 x 2 x 3 text and a 0 b 4 therefore f x x 1 x 2 x 1 x 3 x 2 x 3 Use Simpson s rule x 1 x 2 x 3 from 1 to 3 with 5 intervals factor completely x 1 x 2 x 3 Compute answers using Wolfram s breakthrough technology knowledgebase relied on by millions of students professionals For math science nutrition history geography engineering mathematics linguistics sports
f x x 1 x 2 x 3 in 0 4
f x x 1 x 2 x 3 in 0 4
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Draw The Graph Of The Function Y F x 2 x Between X 1 2 And X 4
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X 1 X 2 X 3 0
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Solution x 3 6x 2 11x 6 is a polynomial function Hence it is continuous on 0 4 and differentiable on 0 4 Thus the function f satisfies the conditions of Lagrange s mean value theorem f c f 4 f 0 4 0 1 3c 2 12c 8 0 B Prove that f x 1 x x2 x3 x4 is positive for all x You will probably need to consider separately the three cases x 0 x 1 and 1 x 0 c Similarly prove that for all positive integers n f x 1 x x2 x2n 1 x2n is positive for all x
F x Natural Language Math Input Extended Keyboard Examples Compute answers using Wolfram s breakthrough technology knowledgebase relied on by millions of students professionals For math science nutrition history geography engineering mathematics linguistics sports finance music f x x 1 x 2 x 3 Following the general formula as derived above f x 1 x 2 x 3 1 x 1 x 3 1 x 2 x 1 Simplifying everything f x x 2 5x 6 x 2 4x 3 x 2 3x 2 f x 3x 2 12x 11 Therefore the derivative simplified is f x 3x 2 12x 11
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Step by step solution Indefinite integral assuming all variables are real Global minimum Decimal form Step by step solution Download Page POWERED BY THE WOLFRAM LANGUAGE Compute answers using Wolfram s breakthrough technology knowledgebase relied on by millions of students professionals A function relates inputs to outputs a function takes elements from a set the domain and relates them to elements in a set the codomain all the outputs the actual values related to are together called the range a function is a special type of relation where every element in the domain is included and
Precalculus Graph f x x 1 x 2 x 3 f x x 1 x 2 x 3 f x x 1 x 2 x 3 Find the point at x 3 x 3 Tap for more steps y 0 y 0 Find the point at x 1 x 1 Tap for more steps y 4 y 4 Find the point at x 0 x 0 Tap for more steps y 6 y 6 Find the point at x 1 x 1 So there is a discontinuity at x 1 f x 1 x 1 So f x 1 x 1 over all Real Numbers is NOT continuous Let s change the domain to x 1 g x 1 x 1 for x 1 So g x IS continuous In other words g x does not include the value x 1 so it
BMW X1 X2 X3 X4 E83 E84 F25 F26 F39
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Find The Range Of F x X 1 x 2 2x 3
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f x x 1 x 2 x 3 in 0 4 - F x Natural Language Math Input Extended Keyboard Examples Compute answers using Wolfram s breakthrough technology knowledgebase relied on by millions of students professionals For math science nutrition history geography engineering mathematics linguistics sports finance music