SOLUTION: Let f(x) = 3x4 − 14x2 + 4x − 5. Find the local maximum and minimum values of f and the values of x at which they occur. Find the intervals on which f is increasing

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Let f(x) = 3x4 − 14x2 + 4x − 5. Find the local maximum and minimum values of f and the values of x at which they occur. Find the intervals on which f is increasing       Log On


   

Question 992402: Let f(x) = 3x4 − 14x2 + 4x − 5.
Find the local maximum and minimum values of f and the values of x at which they occur.
Find the intervals on which f is increasing and on which f is decreasing.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Let f(x) = 3x4 − 14x2 + 4x − 5.
Find the local maximum and minimum values of f and the values of x at which they occur.%28graph%28400%2C400%2C-10%2C10%2C-40%2C10%2C3x%5E4-14x%5E2%2B4x-5%29

Find the intervals on which f is increasing and on which f is decreasing.
f'(x) = 12x^3 - 28x + 4
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Solve 12x^3 - 28x +4 = 0
3x^3 - 7x + 1 = 0
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x = -1.59 or 0.144 or 1.45
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f"(x) = 36x^2 - 28
f"(-1.59) > 0 so min at x = -1.59
f"(0.144) < 0 so max at x = 0.144
f"(1.45) > 0 so min at x = 1.45
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Cheers,
Stan H.
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