The coordinates of one of the points on the graph of the function $f (x) = \frac{x^{3}}{3} - \frac{5 x^{2}}{2} + 7 x - 4$ , where the tangent drawn cuts off intercepts from the coordinate axes which are equal in magnitude but opposite in sign, is

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$(1, \frac{5}{6})$

$(4, \frac{7}{2})$

$(2, \frac{4}{3})$

$(3, \frac{7}{2})$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Since the intercepts are equal in magnitude but opposite in sign ${(\frac{dy}{dx})}_{P} = 1$

$\begin{array}{l} y = f (x) = \frac{x^{3}}{3} - \frac{5 x^{2}}{2} + 7 x - 4 ∴ \frac{dy}{dx} = 1 \\ \Rightarrow x^{2} - 5 x + 7 = 1 \Rightarrow x^{2} - 5 x + 6 = 0 \Rightarrow x = 2, x = 3 ∴ x = 2 \Rightarrow y = f (2) = \frac{8}{3} \\ and x = 3 \Rightarrow y = f (3) = \frac{7}{2}; (2, \frac{8}{3}), (3, \frac{7}{2}) \end{array}$