f(x) = 2x³ - 9x², xe [-1, 3]
f(x) = 6x² - 18x = 6x(x - 18)
when f(x)=0, so, x=0 and x=18
So, the function monotonically increases at [-1,0],
decreases monotonically at [0,3], and reaches its maximum at x=0,
So, when x = -1, f(-1) = 2x(-1)³-9x(-1)² + 5 = -6
x = 0, f(0) = 5
x = 3, f(3) = 2x3³-9 ×3² + 5 = -22
So, M = 5, and m = -22
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Answer:
f(x) = 2x³ - 9x², xe [-1, 3]
f(x) = 6x² - 18x = 6x(x - 18)
when f(x)=0, so, x=0 and x=18
So, the function monotonically increases at [-1,0],
decreases monotonically at [0,3], and reaches its maximum at x=0,
So, when x = -1, f(-1) = 2x(-1)³-9x(-1)² + 5 = -6
x = 0, f(0) = 5
x = 3, f(3) = 2x3³-9 ×3² + 5 = -22
So, M = 5, and m = -22