anonymous
  • anonymous
What are the possible number of positive, negative, and complex zeros of f(x) = 3x4 - 5x3 - x2 - 8x + 4 ?
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Hoping you know derivatives! Find the derivative of the following via implicit differentiation: d/dx(f(x)) = d/dx(3 x^4-5 x^3-x^2-8 x+4) Rewrite the expression: d/dx(f(x)) = d/dx(f(x)): d/dx(f(x)) = d/dx(4-8 x-x^2-5 x^3+3 x^4) The derivative of f(x) is f'(x): f'(x) = d/dx(4-8 x-x^2-5 x^3+3 x^4) Differentiate the sum term by term and factor out constants: f'(x) = d/dx(4)-8 d/dx(x)-d/dx(x^2)-5 d/dx(x^3)+3 d/dx(x^4) The derivative of 4 is zero: f'(x) = -8 (d/dx(x))-d/dx(x^2)-5 (d/dx(x^3))+3 (d/dx(x^4))+0 Simplify the expression: f'(x) = -8 (d/dx(x))-d/dx(x^2)-5 (d/dx(x^3))+3 (d/dx(x^4)) The derivative of x is 1: f'(x) = -(d/dx(x^2))-5 (d/dx(x^3))+3 (d/dx(x^4))-1 8 Use the power rule, d/dx(x^n) = n x^(n-1), where n = 2: d/dx(x^2) = 2 x: f'(x) = -8-5 (d/dx(x^3))+3 (d/dx(x^4))-2 x Simplify the expression: f'(x) = -8-2 x-5 (d/dx(x^3))+3 (d/dx(x^4)) Use the power rule, d/dx(x^n) = n x^(n-1), where n = 3: d/dx(x^3) = 3 x^2: f'(x) = -8-2 x+3 (d/dx(x^4))-5 3 x^2 Simplify the expression: f'(x) = -8-2 x-15 x^2+3 (d/dx(x^4)) Use the power rule, d/dx(x^n) = n x^(n-1), where n = 4: d/dx(x^4) = 4 x^3: f'(x) = -8-2 x-15 x^2+3 4 x^3 Simplify the expression: f'(x) = -8-2 x-15 x^2+12 x^3 Expand the left hand side: Answer: | | f'(x) = -8-2 x-15 x^2+12 x^3

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