1. Tardigrade
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  4. If f(1)=3 and f prime( x ) ≤ 1.4 for 1 ≤ x ≤ 8. The largest possible value which f (8) can have, is

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Q. If $f(1)=3$ and $f^{\prime}( x ) \leq 1.4$ for $1 \leq x \leq 8$. The largest possible value which $f (8)$ can have, is

Application of Derivatives

Solution:

Using LMVT, $\forall$ some $c \in(1,8)$ s.t.
$f ^{\prime}( c )=\frac{ f (8)- f (1)}{7}=\frac{ f (8)-3}{7} \leq 1.4 $
$f (8)=9 \cdot 8+3=12.8 $