Question

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

• A. 12.8
• B. 6.8
• C. 16.8
• D. none

Answer 1

Answer: (A)

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