Suppose that mathrmf(0)=-3 and mathrmf prime( mathrmx) ≤ 5 for all values of mathrmx. Then the largest value which mathrmf(2) can attain is

Question

Suppose that mathrmf(0)=-3 and mathrmf prime( mathrmx) ≤ 5 for all values of mathrmx. Then the largest value which mathrmf(2) can attain is (A) 7 (B) -7 (C) 13 (D) 8

Tardigrade Admin · Accepted Answer

Using LMVT in [0,2] ( mathrmf(2)- mathrmf(0)/2-0)= mathrmf prime( mathrmc) text where mathrmc ∈(0,2) ( mathrmf(2)+3/2) ≤ 5 f (2) ≤ 7

Q. Suppose that $f (0) = - 3$ and $f^{'} (x) \leq 5$ for all values of $x$ . Then the largest value which $f (2)$ can attain is

7

-7

13

8

Using LMVT in $[0, 2]$
$\frac{f ( 2 ) - f ( 0 )}{2 - 0} = f^{'} (c) where c \in (0, 2)$
$\frac{f ( 2 ) + 3}{2} \leq 5$
$f (2) \leq 7$

Q. Suppose that f(0)=−3 and f′(x)≤5 for all values of x. Then the largest value which f(2) can attain is

7

-7

13

8

Using LMVT in [0,2] 2−0f(2)−f(0)​=f′(c) where c∈(0,2) 2f(2)+3​≤5 f(2)≤7

Q. Suppose that $f (0) = - 3$ and $f^{'} (x) \leq 5$ for all values of $x$ . Then the largest value which $f (2)$ can attain is

Using LMVT in $[0, 2]$
$\frac{f ( 2 ) - f ( 0 )}{2 - 0} = f^{'} (c) where c \in (0, 2)$
$\frac{f ( 2 ) + 3}{2} \leq 5$
$f (2) \leq 7$