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9. Find the minimum and maximum values of function y = x³ - 3x² + 6. Also find the values of x at which these occure.
10. The particle's position as a function of time is given as x = 5t² - 9t + 3. Find out the maximum value of position co-ordinate ?

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Solution

Dear Student,
$w e a c n s o l v e o n e q u e s t i o n a t a t i m e . p o s t o t h e r q u e s t i o n i n o t h e r t h r e a d . s o l v i n g 9 . y = x^{3} - 3 x^{2} + 6 \frac{d y}{d x} = 3 x^{2} - 6 x = 0 f o r x = 0 \frac{d^{2} y}{d x^{2}} = 6 x - 6 p u t x = 0 \frac{d^{2} y}{d x^{2}} < 0 h e n c e x = 0 i s t h e p o i n t o f m a x i m a . f o r x = 2 \frac{d^{2} y}{d x^{2}} = 6 x - 6 p u t x = 2 \frac{d^{2} y}{d x^{2}} > 0 h e n c e x = 2 i s t h e p o i n t o f m i n i m a . R e g r d s$

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x = 5 t^{2} - 9 t + 3

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