questionr
Early access
Exams
Joint Entrance Examination
Mathematics
Application of Derivatives
Question 36
Question 36 of 212
Medium
MCQ
The function
f
(
x
)
=
2
x
+
3
(
x
)
2
3
,
x
∈
R
f(x)=2x+3(x{)}^{\frac{2}{3}},x\in R
f
(
x
)
=
2
x
+
3
(
x
)
3
2
,
x
∈
R
, has
A
exactly one point of local minima and no point of local maxima
B
exactly one point of local maxima and exactly one point of local minima
C
exactly two points of local maxima and exactly one point of local minima
D
exactly one point of local maxima and no point of local minima
Check answer
Press A-D to select · Enter to check
Solutions · 1
Post your solution
Official solution
f
(
x
)
=
2
x
+
3
(
x
)
2
3
f
′
(
x
)
=
2
+
2
x
−
1
3
=
2
(
1
+
1
x
1
3
)
=
2
(
x
1
3
+
1
x
1
3
)
\begin{gathered} f(x)=2x+3(x{)}^{\frac{2}{3}} \\ {f}^{'}(x)=2+2{x}^{\frac{-1}{3}} \\ =2(1+\frac{1}{{x}^{\frac{1}{3}}}) \\ =2(\frac{{x}^{\frac{1}{3}}+1}{{x}^{\frac{1}{3}}}) \end{gathered}
f
(
x
)
=
2
x
+
3
(
x
)
3
2
f
′
(
x
)
=
2
+
2
x
3
−
1
=
2
(
1
+
x
3
1
1
)
=
2
(
x
3
1
x
3
1
+
1
)
So, maxima (M) at x =
−
-
−
1 \& minima (m) at x = 0
Answer the question to unlock
Previous
Next