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

Question

If f(1)=3 and f prime( x ) ≤ 1.4 for 1 ≤ x ≤ 8. The largest possible value which f (8) can have, is (A) 12.8 (B) 6.8 (C) 16.8 (D) none

Tardigrade Admin · Accepted Answer

Using LMVT, ∀ some c ∈(1,8) s.t. f prime( c )=( f (8)- f (1)/7)=( f (8)-3/7) ≤ 1.4 f (8)=9 ⋅ 8+3=12.8

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