Application of Derivatives 1 Question 18
18. The curve , touches the -axis at and cuts the -axis at a point , where its gradient is 3 . Find .
(1994, 5M)
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Solution:
- Given,
touches -axis at which implies that -axis is tangent at and the curve is also passes through .
The curve cuts
Now,
Since,
Again, slope of tangent at
Since, the curve passes through
From Eqs. (i) and (ii),
From Eqs. (ii) and (iii),
On adding Eqs. (iv) and (v), we get
On putting