Maxima and Minima — Maths STD 12 Science — Question

1. 75

Sloution:

$\text{f}(\text{x})=\text{x}^{2}+\frac{250}{\text{x}}$

$\text{f}'(\text{x})=2\text{x}-\frac{250}{\text{x}^{2}}$

For the local minima a or maxima. We must have f'(x) = 0

 $=2\text{x}-\frac{250}{\text{x}^{2}}=0$

⇒ x = 5

$=2\text{x}-\frac{250}{\text{x}^{2}}=0$

$\text{f}''(\text{x})=2+\frac{500}{\text{x}^{3}}$

$\text{f}''(\text{x})=2+\frac{500}{125}>0$

function has minima at x = 5

f(5) = 75.