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COMEDK2023Morning ShiftMathematicsApplication of DerivativesActual

The approximate value of f(5.001) , where f(x)=x^3-7 x^2+10

Options

  1. A-37.335
  2. B-39.995
  3. C-38.995
  4. D-40.995

Correct answer

B. -39.995

Step-by-step solution

The function is given by f(x) = x³ - 7x² + 10 . The approximate value of f(x + x) is given by f(x) + f'(x) x . Here, x = 5 and x = 0.001 . First, calculate f(5) = (5)³ - 7(5)² + 10 = 125 - 7(25) + 10 = 125 - 175 + 10 = -40 . Next, find the derivative f'(x) = 3x² - 14x . Evaluate f'(5) = 3(5)² - 14(5) = 3(25) - 70 = 75 - 70 = 5 . Now, calculate the approximation f(5.001) f(5) + f'(5) x = -40 + 5(0.001) = -40 + 0.005 = -39.995 . Answer: -39.995

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