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COMEDK2024MathematicsApplication of Derivatives

Find the approximate value of function f(x)=x^3-5 x+10 at x=3.001 .

Options

  1. A31.023
  2. B22.007
  3. C31.23
  4. D22.07

Correct answer

D. 22.07

Step-by-step solution

We can write 3.001 as x=3 and x=0.001 and use the relation aligned & f(x+ x) f(x)+ x f^ (x) & f^ (x)=3 x^2-5 aligned Now, aligned f(3 & +0.001) f(3)+(0.001) (f^ (5) ) & 27-15+10+0.001(75-5) & 27-5+ 70 1000 & 22+0.07 22.07 aligned

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