SATHEE: Indefinite Integration 1 Question 44

Indefinite Integration 1 Question 44

45. If $f^{''} (x) < 0, \forall x \in (a, b)$ , and $(c, f (c))$ is point of maxima, where $c \in (a, b)$ , then $f^{'} (c)$ is

(a) $\frac{f (b) - f (a)}{b - a}$

(b) $3 \frac{f (b) - f (a)}{b - a}$

(d) 0

Show Answer

Solution:

$F^{'} (c) = (b - a) f^{'} (c) + f (a) - f (b)$

$\begin{aligned} F^{''} (c) & = f^{''} (c) (b - a) < 0 \\ \Rightarrow F^{'} (c) & = 0 \Rightarrow f^{'} (c) = \frac{f (b) - f (a)}{b - a} \end{aligned}$

Indefinite Integration 1 Question 44

45. If $f^{''} (x) < 0, \forall x \in (a, b)$ , and $(c, f (c))$ is point of maxima, where $c \in (a, b)$ , then $f^{'} (c)$ is

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Indefinite Integration 1 Question 44

45. If f′′(x)<0,∀x∈(a,b), and (c,f(c)) is point of maxima, where c∈(a,b), then f′(c) is

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

45. If $f^{''} (x) < 0, \forall x \in (a, b)$ , and $(c, f (c))$ is point of maxima, where $c \in (a, b)$ , then $f^{'} (c)$ is