Question

Tentukan nilai maximal dari f(x) = 5x³- 3x⁵ pada interval -2 ≤ x ≤ 2

Answer 1

f(x) = 5x³- 3x⁵ pada interval -2 ≤ x ≤ 2
f'(x) = 0
15x² - 15x^4 = 0
15x²(1 - x²) = 0
15x² = 0 maka x = 0 atau x² - 1 = 0 maka x = 1 atau x = -1
f(-2) = 5(-2)³ - 3(-2)^5 = -40 + 96 = 56 maksimal
f(-1) = 5(-1)³ - 3(-1)^5 = -5 + 3 = -2
f(0) = 0
f(1) = 5(1)³ - 3(1)^5 = 5 - 3 = 2
f(2) = 5(2)³ - 3(2)^5 = 40 - 96 = - 56