If gt- maxt3-6t2-9t-3-0 t-0-3- 4-t t-3-4- - find the point of non-differentiable is

Explanation for the correct option.Given, g(t)={[ max(t^3 6t^2+9t 3,0) t∈[0,3]; 4 t t∈[3,4] ]..y=t^3 6t^2+9 ...

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Standard XII

Mathematics

Inverse of a Function

If gt=[ ...

Question

If $g (t) = \{\begin{cases} m a x (t^{3} - 6 t^{2} + 9 t - 3, 0) t \in [0, 3] \\ 4 - t t \in [3, 4] \end{cases}$ , find the point of non-differentiable is

$1$

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$3$

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$2$

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$4$

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Solution

The correct option is B
$3$

Explanation for the correct option.
Given, $g (t) = \{\begin{cases} m a x (t^{3} - 6 t^{2} + 9 t - 3, 0) t \in [0, 3] \\ 4 - t t \in [3, 4] \end{cases}$ .
$y = t^{3} - 6 t^{2} + 9 t - 3$
Now, differentiate w.r.t. $t$ .
$\begin{array}{rcl} \frac{d}{d t} y & = & 3 t^{2} - 12 t + 9 \\ = & 3 (t^{2} - 4 t + 3) \\ = & 3 (t^{2} - t - 3 t + 3) \\ = & 3 (t (t - 1) - 3 (t - 1)) \\ = & 3 (t - 1) (t - 3) \end{array}$
So, there are $3$ points of non-differentiable.
Hence, the correct option is B.

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If g(t)=maxt3-6t2+9t-3,0t∈0,34-tt∈3,4, find the point of non-differentiable is

The correct option is B 3Explanation for the correct option.Given, g(t)=maxt3-6t2+9t-3,0t∈0,34-tt∈3,4.y=t3-6t2+9t-3Now, differentiate w.r.t. t.ddty=3t2-12t+9=3t2-4t+3=3t2-t-3t+3=3tt-1-3t-1=3t-1t-3So, there are 3 points of non-differentiable.Hence, the correct option is B.

If $g (t) = \{\begin{cases} m a x (t^{3} - 6 t^{2} + 9 t - 3, 0) t \in [0, 3] \\ 4 - t t \in [3, 4] \end{cases}$ , find the point of non-differentiable is