What is taylor (-3x+14)^{4/3},2 ?

The answer to taylor (-3x+14)^{4/3},2 is 16-8(x-2)+1/2 (x-2)^2+1/24 (x-2)^3+5/768 (x-2)^4+\ldots

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taylor (-3x+14)^{4/3},2

taylor

(- 3 x + 14)^{\frac{4}{3}}, 2

16 - 8 (x - 2) + \frac{1}{2} (x - 2)^{2} + \frac{1}{24} (x - 2)^{3} + \frac{5}{768} (x - 2)^{4} + \dots

Solution steps

Apply the Taylor Formula

= 16 + \frac{\frac{d}{d x} ( ( - 3 x + 14 ) ^{\frac{4}{3}} ) ( 2 )}{1 !} (x - 2) + \frac{\frac{d ^{2}}{d x ^{2}} ( ( - 3 x + 14 ) ^{\frac{4}{3}} ) ( 2 )}{2 !} (x - 2)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( - 3 x + 14 ) ^{\frac{4}{3}} ) ( 2 )}{3 !} (x - 2)^{3} + \dots

Evaluate Derivatives

= 16 + \frac{- 8}{1 !} (x - 2) + \frac{1}{2 !} (x - 2)^{2} + \frac{\frac{1}{4}}{3 !} (x - 2)^{3} + \frac{\frac{5}{32}}{4 !} (x - 2)^{4} + \dots

Refine

= 16 - 8 (x - 2) + \frac{1}{2} (x - 2)^{2} + \frac{1}{24} (x - 2)^{3} + \frac{5}{768} (x - 2)^{4} + \dots

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What is taylor (-3x+14)^{4/3},2 ?
The answer to taylor (-3x+14)^{4/3},2 is 16-8(x-2)+1/2 (x-2)^2+1/24 (x-2)^3+5/768 (x-2)^4+\ldots