Question

function f(x) = x - 3x + 4 has minimum value at x = ...​

Answer 1

f(x) = x² - 3x + 4

for minimum value of f(x),

$\frac{df(x)}{dx} = 0 \\ \\ so \\ \frac{df(x)}{dx} \\ = {f}^{ |} (x) \\ = \frac{d}{dx} ( {x}^{2} - 3x + 4) \\ = \frac{d {x}^{2} }{dx} - \frac{d(3x)}{dx} + \frac{d(4)}{dx} \\ = 2 {x}^{2 - 1} - 3 \times 1 {x}^{1 - 1} + 0 \\ = 2 {x}^{1} - 3 {x}^{0} = 2x - 3 \times 1 = 2x - 3 \\ = 2x - 3$

hence,

$2x - 3 = 0 \\ \: \: \: \: \: \: \: \: 2x = 3 \\ \: \: \: \: \: \: \: \: \: \: x = \frac{3}{2}$

Hence, at x = 3/2, f(x) assumes the minimum value.