Let f be a twice differentiable function on (1,6) . If f (2)=8, f'(2)=5, f prime( x ) ≥ 1 and f''(x) ≥ 4, for all x ∈(1,6), then :

Question

Let f be a twice differentiable function on (1,6) . If f (2)=8, f'(2)=5, f prime( x ) ≥ 1 and f''(x) ≥ 4, for all x ∈(1,6), then : (A) f (5) ≤ 10 (B) f '(5)+ f ''(5) ≤ 20 (C) f (5)+ f'(5) ≥ 28 (D) f (5)+ f'(5) ≤ 26

Tardigrade Admin · Accepted Answer

f(2)=8, f'(2)=5, f'(x) ≥ 1, f''(x) ≥ 4, ∀ x ∈(1,6) f''(x)=(f'(5)-f'(2)/5-2) ≥ 4 ⇒ f'(5) ≥ 17 dots(1) f'(x)=(f(5)-f(2)/5-2) ≥ 1 ⇒ f(5) ≥ 11 dots(2) overlinef'(5)+f(5) ≥ 28

Q. Let $f$ be a twice differentiable function on $(1, 6) .$ If $f (2) = 8, f^{'} (2) = 5, f^{'} (x) \geq 1$ and $f^{''} (x) \geq 4,$ for all $x \in (1, 6),$ then :

$f (5) \leq 10$

$f^{'} (5) + f^{''} (5) \leq 20$

$f (5) + f^{'} (5) \geq 28$

$f (5) + f^{'} (5) \leq 26$

Q. Let f be a twice differentiable function on (1,6). If f(2)=8,f′(2)=5,f′(x)≥1 and f′′(x)≥4, for all x∈(1,6), then :

f(5)≤10

f′(5)+f′′(5)≤20

f(5)+f′(5)≥28

f(5)+f′(5)≤26

f(2)=8,f′(2)=5,f′(x)≥1,f′′(x)≥4,∀x∈(1,6) f′′(x)=5−2f′(5)−f′(2)​≥4 ⇒f′(5)≥17…(1) f′(x)=5−2f(5)−f(2)​≥1 ⇒f(5)≥11…(2) f′(5)+f(5)≥28​

Q. Let $f$ be a twice differentiable function on $(1, 6) .$ If $f (2) = 8, f^{'} (2) = 5, f^{'} (x) \geq 1$ and $f^{''} (x) \geq 4,$ for all $x \in (1, 6),$ then :

$f (5) \leq 10$

$f^{'} (5) + f^{''} (5) \leq 20$

$f (5) + f^{'} (5) \geq 28$

$f (5) + f^{'} (5) \leq 26$