Find maximum or minimum of 2x - 7 - 5x2.

1.	Find maximum or minimum of 2x - 7 - 5x2.
Answer» Let y = 2x - 7 5x² ⇒ y ′= 2 − 10x = 0, for max/min ⇒ x = 51 Also y′′ = −10 < 0 so maximum value of y is = y(\(\frac{1}{5}\)) = 2⋅\(\frac{1}{5}\) −7 − 5 ⋅ \(\frac{1}{25}\) = \(\frac{2}{5}\) − 7 − \(\frac{1}{5}\) = \(\frac{1}{5}\) − 7 = −\(\frac{34}{7}\) And minimum value of y will be −∞

Answer»

Let y = 2x - 7 5x²

⇒ y ′= 2 − 10x = 0, for max/min

⇒ x = 51

Also y′′ = −10 < 0

so maximum value of y is = y(\(\frac{1}{5}\)) = 2⋅\(\frac{1}{5}\) −7 − 5 ⋅ \(\frac{1}{25}\)

= \(\frac{2}{5}\) − 7 − \(\frac{1}{5}\)

= \(\frac{1}{5}\) − 7

= −\(\frac{34}{7}\)

And minimum value of y will be −∞

Discussion