In parts (a)(c), sketch a continuous curve y = f(x)with the stated properties.(a) f(2) =
Chapter 4, Problem 39(choose chapter or problem)
In parts (a)-(c), sketch a continuous curve \(y=f(x)\) with the stated properties.
(a) \(f(2)=4, f^{\prime}(2)=0, f^{\prime \prime}(x)>0 \text { for } x\)
(b) \(f(2)=4, f^{\prime}(2)=0, f^{\prime \prime}(x)<0 x<2, f^{\prime \prime}(x)>0 \text { for } x>2\)
(c) \(f(2)=4, f^{\prime}(2)=0, f^{\prime \prime}(x)>0 \text { for } x \neq 2\) and \(\lim _{x \rightarrow 2^{+}} f^{\prime}(x)=+\infty, \lim _{x \rightarrow 2^{-}} f^{\prime}(x)=-\infty\)
Equation Transcription:
for
for
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and
Text Transcription:
y = f(x)
f(2) = 4, f’(2) = 0, f’’(x) > 0 for x
f(2) = 4, f’ (2) = 0, f’’(x) < 0 x <2, f’’(x) > 0 for x > 2
f(2) = 4, f’(2) = 0, f’’(x) > 0 for x neq 2 and lim _x 2^+ f’(x) = + infty, lim _x 2^- f(x) = - infty
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