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  4. The co-ordinates of point(s) on the graph of the function, f(x)=(x3/3)-(5 x2/2)+7 x-4 where the tangent drawn cut off intercepts from the co-ordinate axes which are equal in magnitude but opposite in operatornamesign, is

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Q. The co-ordinates of point(s) on the graph of the function, $f(x)=\frac{x^{3}}{3}-\frac{5 x^{2}}{2}+7 x-4$ where the tangent drawn cut off intercepts from the co-ordinate axes which are equal in magnitude but opposite in $\operatorname{sign}$, is

Application of Derivatives

Solution:

Slope of tangent $=1$
$f '( x )=1 $
$ x ^{2}-5 x +7=1 $
$x ^{2}-5 x +6=0 $
$ x =2,3$
$f (2)=\frac{8}{3}, $
$f (3)=\frac{7}{2}$