Consider function f (x) = 8x^2 - 7x + 5 on interval [-6, 6] . value of c that satisfies conclusion o

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5. Continuity and Differentiation

hard

Consider the function $f (x) = 8x^2 - 7x + 5$ on the interval $[-6, 6]$. The value of $c$ that satisfies the conclusion of the mean value theorem, is

A

$- 7/8$

B

$-4$

C

$7/8$

D

$0$

Solution

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

$=\frac{{(8\,\cdot\,36 – 7\,\cdot\,6 + 5) – (8.36 + 7.6 + 5)}}{{12}} $

$= -\frac{{2\,\cdot\,7\,\cdot\,6}}{{12}} = – 7$

$16c = 0\,==>\,c = 0$

Standard 12

Mathematics

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