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Global Maxima

If y=fx is ...

Question

If $y = f (x)$ is represented as $x = g (t) = t^{5} - 5 t^{3} - 20 t + 7$ and $y = h (t) = 4 t^{3} - 3 t^{2} - 18 t + 3, (- 2 < t < 2)$ , then max $f (x)$ is equal to

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Solution

$y = f (x)$
Max $f (x) = y_{m a x}$
$y = 4 t^{3} - 3 t^{2} - 18 t + 3$ , for $(- 2 < t < 2)$
$\frac{d y}{d t} = 12 t^{2} - 6 t - 18$
For $y_{m a x}, \frac{d y}{d t} = 0$
$\Rightarrow 2 t^{2} - t - 3 = 0$ , gives
$t = - 1, \frac{3}{2}$
At $t = - 1, y_{m a x} = 14$

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Similar questions

y = f (x)

x = t^{5} - 5 t^{3} - 20 t + 7

y = 4 t^{3} - 3 t^{2} - 18 t + 3

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