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Provide solution for rd sharma maths class 12 chapter 16 Increasing and decreasing functions exercise multiple choice quection, question 10

Answers (1)

Correct option (c)

Hint: Differentiate the given function w.r.t  x  then check the given conditions

Given:f(x)=x^{3}-6 x^{2}+15 x+3

Explanation: It is given that

f(x)=x^{3}-6 x^{2}+15 x+3

Now,Differentiate (i) w.r.t  x

\begin{aligned} &f^{\prime}(x)=3 x^{2}-12 x+15 \\ &f^{\prime}(x)=3\left(x^{2}-4 x+5\right) \\ &f^{\prime}(x)=3\left[(x-2)^{2}+1\right]>0 \end{aligned} 

Since \begin{aligned} &f^{\prime}(x)>0 \end{aligned} , so \begin{aligned} &f(x) \end{aligned}  is increasing function.

As \begin{aligned} &f(x) \end{aligned} is increasing, it is invertible

Thus, \begin{aligned} &f(x) \end{aligned} is invertible function.

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