Question

use find the local maximum and local minimum both first and second derivative i) f (x) = x²- x - logx
ii) f(x) = √x- 4√x​

Answer 1

Answer:

Given,

f(x)=(x−5)

4

differentiating the above function, we get,

f

′

(x)=4(x−5)

3

f

′

(x)=0

⇒4(x−5)

3

=0

x−5=0

∴x=5

And, since f

′

(x)=4(x−5)

3

then

f

′

(x)≤0whenx≤5

f

′

(x)>0whenx>5

∴x=5 is point of minima

now,

f(5)=((5)−5)

4

∴f(5)=0

x=5 is a point of local minimum, local minimum value=0.