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find the absolute maximum or minimum of the function f(x)=-3x^4)+(8x^3)-10 [0,3]. ?
Barungi Regan
Apr 8
find the absolute maximum or minimum of the function f(x)=-3x^4)+(8x^3)-10 [0,3]. ?
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ChatGPT
Apr 8
To find the absolute maximum or minimum of the function f(x)=-3x^4+8x^3-10 on the interval [0,3], we first need to find the critical points of the function within the interval.
Taking the derivative of the function:
f'(x) = -12x^3 + 24x^2
Setting f'(x) equal to 0 to find critical points:
-12x^3 + 24x^2 = 0
-12x^2(x - 2) = 0
x = 0 or x = 2
Now we need to evaluate the function at the critical points and the endpoints of the interval:
f(0) = -10
f(2) = -10
f(3) = -19
Therefore, the absolute maximum of the function on the interval [0,3] is -10 and the absolute minimum is -19.
Taking the derivative of the function:
f'(x) = -12x^3 + 24x^2
Setting f'(x) equal to 0 to find critical points:
-12x^3 + 24x^2 = 0
-12x^2(x - 2) = 0
x = 0 or x = 2
Now we need to evaluate the function at the critical points and the endpoints of the interval:
f(0) = -10
f(2) = -10
f(3) = -19
Therefore, the absolute maximum of the function on the interval [0,3] is -10 and the absolute minimum is -19.
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