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COMEDK2021MathematicsApplication of Derivatives

The approximate value of f(5.001) , where f(x)=x³-7 x²+15 is

Options

  1. A-34.995
  2. B-33.995
  3. C-33.335
  4. D-35.995

Correct answer

A. -34.995

Step-by-step solution

The function is given by f(x) = x³ - 7x² + 15 . Using the linear approximation formula f(x + x) f(x) + f'(x) x , we set x = 5 and x = 0.001 . First, calculate f(5) = (5)³ - 7(5)² + 15 = 125 - 7(25) + 15 = 125 - 175 + 15 = -35 . Next, find the derivative f'(x) = 3x² - 14x . Evaluate the derivative at x = 5 : f'(5) = 3(5)² - 14(5) = 3(25) - 70 = 75 - 70 = 5 . Now, calculate the approximate value f(5.001) f(5) + f'(5) x = -35 + 5(0.001) = -35 + 0.005 = -34.995 . Answer: -34.995

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