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Provide an appropriate response.Consider the quartic function f(x) = ax4 + bx3 + cx2 + dx + e, a 0. ...
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Provide an appropriate response.Consider the quartic function f(x) = ax4 + bx3 + cx2 + dx + e, a 0. ...
Provide an appropriate response.
Consider the quartic function f(x) = ax
^{4}
+ bx
^{3}
+ cx
^{2}
+ dx + e, a ≠ 0. Must this function have at least one critical point? Give reasons for your answer. (Hint: Must
for some x?) How many local extreme values can f have?
Textbook
Calculus: Early Transcendentals
Edition:
3
^{rd}
Authors:
Briggs, Cochran, Gillett, Schulz
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More questions for this book are
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Yes. The derivative is cubic: 4ax
^{3}
+ 3bx
^{2}
+ 2cx + d. The derivative approaches -∞ as x approaches
and it approaches ∞ as x approaches ∞. By the Intermediate Value Theorem, f'(x) must equal zero at at least one point on the interval -∞ ≤ x ≤ ∞.
1
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