Application of Derivatives 4 Question 17

18. The number of points in (,) for which

x2xsinxcosx=0, is

(2013 Adv.)

(a) 6

(b) 4

(c) 2

(d) 0

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Answer:

Correct Answer: 18. (c)

Solution:

  1. PLAN The given equation contains algebraic and trigonometric functions called transcendental equation. To solve transcendental equations we should always plot the graph for LHS and RHS.

Here, x2=xsinx+cosx

Let f(x)=x2 and g(x)=xsinx+cosx

We know that, the graph for f(x)=x2

To plot,

g(x)=xsinx+cosxg(x)=xcosx+sinxsinxg(x)=xcosxg(x)=xsinx+cosx

 Put g(x)=0xcosx=0x=0,π2,3π2,5π2,7π2

At x=0,3π2,7π2,,f(x)>0, so minimum

At x=π2,5π2,9π2,,f(x)<0, so maximum

So, graph of f(x) and g(x) are shown as

So, number of solutions are 2.



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