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  • The coordinate of the point(s) on the graph of the function <img alt="f(x)=\frac{x^3}{3}-\frac{5 x^2}{2}+7 x-4" src="https://entrancecorner.oncodecogs.com/gif.latex?f%28x%29%3D%5Cfrac%7Bx%5E3%7D%7B

The coordinate of the 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 coordinate axes which are equal in magnitude but opposite in sign, is

Option: 1

\left(2, \frac{8}{3}\right)


Option: 2

\left(3, \frac{7}{2}\right)


Option: 3

\left(1, \frac{5}{6}\right)


Option: 4

None of these


Answers (1)

best_answer

Since, intercepts are equal in magnitude but opposite in sign

\Rightarrow \: \: \: \: \: \: \: \: \: \quad\left[\frac{d y}{d x}\right]_P=1

Now,             \frac{d y}{d x}=x^2=5 x+7=1

\begin{array}{lc} \Rightarrow &\: \: \: \: \: \: \: \: \: \: \: \: \: x^2-5 x+6=0 \\ \Rightarrow & x=2 \text { or } 3 \end{array}

Posted by

Kuldeep Maurya

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