Home
Class 12
MATHS
If f'(x)=(x-a)^(2010)(x-b)^(2009) and ag...

If `f'(x)=(x-a)^(2010)(x-b)^(2009) and agtb`, then

A

f(x) has relative maxima at x = b

B

f(x) has relative minima at x = b

C

f(x) has relative maxima at x = a

D

f(x) has neither maxima, nor minima at x = a

Text Solution

Verified by Experts

The correct Answer is:
B, D
Given `f'(x)=(x-a)^(2010)(x-b)^(2009) and a gtb`
Sign scheme of f'(x) is

From sign scheme, x = b is point of minima and x = a is neither maxima nor minima.
Promotional Banner

Topper's Solved these Questions

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Comprehension Type|6 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Comprehension Type|6 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Linked comprehension Type|2 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Numberical Value Type|5 Videos

Similar Questions

Explore conceptually related problems

If f(x)=(a(x-b))/(a-b)+(b(x-a))/(b-a) , then prove that f(a) + f(b) = a + b.

Let f: RvecR ,f(x)=(x-a)/((x-b)(x-c)),b > cdot If f is onto, then prove that a in (b , c)dot

If f(x)=e^(x+a),g(x)=x^(b^2)and h(x)=e^(b^2x), find the value of (g[f(x)])/(h(x)).

If f(x)=a.(x-b)/(a-b)+b.(x-a)/(b-a) , show that, " "f(a)+f(b)=f(a+b) .

If f(x)=a(x-b)/(a-b)+b.(x-a)/(b-a) then show that f(a)+f(b)=f(a+b).

If f(x)=(x-a)/x+x/(x-b) , then find f((a+b)/2) .

If f(x)=e^(x+a) , g(x)=x^(b^2) and h(x)=e^(b^2x) ,show that (g[f(x)])/(h(x))=e^(ab^2)

If f(x) = e^(x + a) , g(x) = x^(b^2) and h(x) = e^(b^2 x) , then find the value of (g{f(x)})/(h(x))

If f(x)=(x^(2)+3x+2)(x^(2)-7x+a) and g(x)=(x^(2)-x-12)(x^(2)+5x+b) , then the value of a and b , if (x+1)(x-4) is H.C.F. of f(x) and g(x) is (a) a=10 : b=6 (b) a=4 : b=12 (c) a=12 : b=4 (d) a=6 : b=10

Let f be a function defined on R (the set of all real numbers) such that f^(prime)(x)=2010(x-2009)(x-2010)^2(x-2011)^3(x-2012)^4, for all x in Rdot If g is a function defined on R with values in the interval (0,oo) such that f(x)=ln(g(x)), for all x in R , then the number of point is R at which g has a local maximum is ___