Mean value theorems

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Question

Consider the function $f (x) = 8 x^{2} - 7 x + 5$ on the interval $[- 6, 6] .$ the value of c satisfying the conclusion of Lagrange’s mean value theorem is ______________.

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Solution

$f^{'} (c) = 16 c - 7$
           $= \frac{f (6) - f (- 6)}{12}$

             $= \frac{(8 \times 36 - 7 \times 6 + 5) - (8 \times 36 - 7 \times 6 + 5)}{12}$

              $= - \frac{2 \times 7 \times 6}{12} = - 7$

$\Rightarrow c = 0$

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Mean value theorems

Remember concepts with our Masterclasses.

Consider the function f(x)=8x2−7x+5 on the interval [−6,6]. the value of c satisfying the conclusion of Lagrange’s mean value theorem is ______________.

f'(c)=16c−7 =f(6)−f(−6)12 =(8×36−7×6+5)−(8×36−7×6+5)12 =−2×7×612=−7 ⇒c=0

Ready to Test Your Skills?

free study material

Consider the function $f (x) = 8 x^{2} - 7 x + 5$ on the interval $[- 6, 6] .$ the value of c satisfying the conclusion of Lagrange’s mean value theorem is ______________.

$f^{'} (c) = 16 c - 7$
$= \frac{f (6) - f (- 6)}{12}$

$= \frac{(8 \times 36 - 7 \times 6 + 5) - (8 \times 36 - 7 \times 6 + 5)}{12}$

$= - \frac{2 \times 7 \times 6}{12} = - 7$

$\Rightarrow c = 0$