Home
Class 12
MATHS
Let f(x) be a polynomial of degree 3 ...

Let `f(x)` be a polynomial of degree 3 having a local maximum at `x=-1.` If `f(-1)=2,\ f(3)=18 ,` and `f^(prime)(x)` has a local minimum at `x=0,` then distance between `(-1,\ 2)a n d\ (a ,\ f(a)),` which are the points of local maximum and local minimum on the curve `y=f(x)` is `2sqrt(5)` `f(x)` is a decreasing function for `1lt=xlt=2sqrt(5)` `f^(prime)(x)` has a local maximum at `x=2sqrt(5)` `f(x)` has a local minimum at `x=1`

A

the distance between (-1,2) and (a,f(a)), where x=a is the point of minima is `2sqrt5`

B

f(x) is increasing for `x in [1,2sqrt5[`

C

f(x) has local minima at x=1

D

the value of f(0)=5

Text Solution

Verified by Experts

The correct Answer is:
B, C
Promotional Banner

Similar Questions

Explore conceptually related problems

Find all the points of local maxima and local minima of the function f(x)=(x-1)^(3)(x+1)^(2)

Find the local maximum and local minimum value of f(x)= x^(3)-3x^(2)-24x+5

If f(x) is a cubic polynomil which as local maximum at x=-1 . If f(2)=18,f(1)=-1 and f'(x) has minimum at x=0 then

Let f(x)=sinx-x" on"[0,pi//2] find local maximum and local minimum.

Find the local maximum and local minimum value of f(x)=sec x+log cos^(2)x,0

Write True/False: If f'( c )=0 then f(x) has a local maximum or a local minimum at x=c