Question

If \[ f(x)=x^3-19x+30 \] is a real valued function with domain \([-4,1]\), then the value of \(c\) according to Lagrange's Mean Value Theorem for \(f(x)\) is

• A. \(\sqrt{4.33}\)
• B. \(-2\)
• C. \(-\sqrt{4.33}\)
• D. \(-3\)

Hint:

For LMVT problems, first compute the average rate of change \[ \frac{f(b)-f(a)}{b-a}, \] then equate it to \(f'(c)\). Finally, choose the solution that lies inside the open interval \((a,b)\).

Answer 1

The Correct Option is C