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

Question

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 (A) (2,8 / 3) (B) (3,7 / 2) (C) (1,5 / 6) (D) none

Tardigrade Admin · Accepted Answer

Slope of tangent =1 f '( x )=1 x 2-5 x +7=1 x 2-5 x +6=0 x =2,3 f (2)=(8/3), f (3)=(7/2)

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 $sign$ , is

$(2, 8/3)$

$(3, 7/2)$

$(1, 5/6)$

none

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

Q. The co-ordinates of point(s) on the graph of the function, f(x)=3x3​−25x2​+7x−4 where the tangent drawn cut off intercepts from the co-ordinate axes which are equal in magnitude but opposite in sign, is

(2,8/3)

(3,7/2)

(1,5/6)