Question

f(x) = 3x² - 2x + 4. find minima and maxima ​

Answer 1

Answer:

(0.333,3.667)

Step-by-step explanation:

This equation is squared meaning it only has one curve, if you graph it the minima will be (0.333,3.667)

Answer 2

Answer:

Differentiate with respect to x

f'(x) = 6x - 2...........[1]

For max and min

f'(x) = 0

6x - 2 = 0

x = 1/3.

Differentiate [1] with respect to x

f''(x) = 6 > 0

Hence, f(x) is minimum at x = 1/3.

So minimum value is

$f (\frac{1}{3} ) = 3 {( \frac{1}{3}) }^{2} - 2 \times \frac{1}{3} + 4 \\ = 3 \times \frac{1}{9} - \frac{2}{3} + 4 \\ = \frac{1}{3} - \frac{2}{3} + 4 \\ = \frac{11}{3}$