Question

find the maximum and minimum of the x²-7x+10​

Answer 1

Answer:

$minima = - \frac{9}{4} \\at\:\: x\:\:=7/2 \\ \\ maxima \: not \: exists.$

Step-by-step explanation:

$y = {x}^{2} -7 x + 10 \\ \\ \\ \frac{dy}{dx} = 2x - 7 \\ \\ 2x - 7 = 0 \\ \\ x = \frac{7}{2} \\ \\ \\ \frac{d {y}^{2} }{d {x}^{2} } = 2 > 0 \\ \\ minima = {( \frac{7}{2} )}^{2} - 7( \frac{7}{2} ) + 10 \\ \\ = \frac{49}{4} - \frac{49}{2} + 10 \\ \\ = \frac{49 - 98 + 40}{4} \\ \\ = \frac{40 - 49}{4} \\ \\ = - \frac{9}{4} .$