if f(0)=12,f(3)=6 and f(4)=8,then linear interpolation function f(x)=?

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if f(0)=12,f(3)=6 and f(4)=8,then linear interpolation function f(x)=? ​

Gianna · Answer

SOLUTION        GIVEN      f(0) = 12 , f(3) = 6 and f(4) = 8      TO         DETERMINE      The linear interpolation function f(x)      EVALUATION      Here it is given that     f(0) = 12 , f(3) = 6 and f(4) = 8    Now     ω(x)     = ( x - 0 ) ( x - 3 ) ( x - 4 )     = x(x - 3)(x - 4 )      ∴ ω'(x)    = (x - 3)(x - 4 ) + x(x - 4 ) + x(x - 3)    ω'(0) = 12    ω'(3) = - 3    ω'(4) = 4    Now the required polynomial        displaystyle  sf{ =   omega(x)  sum  :   frac{f(x_r) }{(x - x_r){ omega}^{'} (x_r) } }      displaystyle  sf{ =  x(x - 3)(x - 4)  bigg[   :    frac{12}{12(x - 0)} +   frac{6}{ - 3(x - 3)}  +   frac{8}{4(x - 4)}   :  bigg]  }      displaystyle  sf{ =  x(x - 3)(x - 4)  bigg[   :    frac{1}{x}  -   frac{2}{ (x - 3)}  +   frac{2}{(x - 4)}   :  bigg]  }      displaystyle  sf{ =  (x - 3)(x - 4) - 2x(x - 4) + 2x(x - 3)}      sf{ =  {x}^{2} - 5x + 12 }       ━━━━━━━━━━━━━━━━       Learn more from Brainly :-     1. write a quadratic polynomial sum of whose zeroes is 2 and product is -8     https://brainly.in/question/25501039    2. The quadratic polynomial where α=5+2√6 and αβ=1 is     https://brainly.in/question/24697408

Amara

Use division algorithm to find all the zeroes of the polynomial p(x) =6×4 -10×3 – 25×2 +35x+14.it is being given that √7/ √2,-√7/

fill in the blanks:i, out of six consecutive natural numbers,if the sum of first three is 27, the sum of other three is___________

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if f(0)=12,f(3)=6 and f(4)=8,then linear interpolation function f(x)=?​