Question

The minimum value of the function f(x) = 13 - 14x + 9x² is ______

Options

• `59/9`

• `-59/9`

• `-68/9`

• `68/9`

Answer 1

The minimum value of the function f(x) = 13 - 14x + 9x² is `underline(68/9)`.

Explanation:

f(x) = 13 - 14x + 9x² 

∴ f'(x) = -14 + 18x

For maximum or minimum,

f'(x) = 0 ⇒ -14 + 18x = 0

⇒ `x = 7/9`

Now, f''(x) = 18 > 0

∴ f(x) is minimum at x = `7/9`.

∴ `[f(x)]_"min" = f(7/9) = 13 - 98/9 + (9 xx 49)/81 = 68/9`