JEE 2024 — Mathematics PYQ
JEE | Mathematics | 2024The function f(x)=2x+3x32, x∈R has
Choose the correct answer:
- A.
exactly one point of local minima and no point of local maxima
- B.
exactly one point of local maxima and no point of local minima
- C.
exactly one point of local maxima and exactly one point of local minima
(Correct Answer) - D.
exactly two points of local maxima and exactly one point of local minima
exactly one point of local maxima and exactly one point of local minima
Explanation
f(x)=2x+3x32
Diff. w.r.t. x,
f′(x)=2+2x−31=2+x312
=2(x31x31+1)
f′(x)=0
x31+1=0
x=−1
Critical point: x=−1
Exactly are point local maxima & exactly one point local minima
Explanation
f(x)=2x+3x32
Diff. w.r.t. x,
f′(x)=2+2x−31=2+x312
=2(x31x31+1)
f′(x)=0
x31+1=0
x=−1
Critical point: x=−1
Exactly are point local maxima & exactly one point local minima