Application of Derivatives 4 Question 1

1. Let f(x)=5|x2| and g(x)=|x+1|,xR. If f(x) attains maximum value at α and g(x) attains minimum value of β, then limxαβ(x1)(x25x+6)x26x+8 is equal to

(a) 1/2

(b) 3/2

(c) 1/2

(d) 3/2

(2019 Main, 12 April II)

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Answer:

Correct Answer: 1. (a)

Solution:

  1. Given functions are f(x)=5|x2|

and g(x)=|x+1|, where xR.

Clearly, maximum of f(x) occurred at x=2, so α=2.

and minimum of g(x) occurred at x=1, so β=1.

αβ=2 Now, limxαβ(x1)(x25x+6)x26x+8=limx2(x1)(x3)(x2)(x4)(x2)[αβ=2]=limx2(x1)(x3)(x4)=(21)(23)(24)=1×(1)(2)=12



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