Problem 3. Determine whether each of the following...

Problem 3. Determine whether each of the following statements is TRUE or FALSE (a) If $f'(c)f''(c) = 0$ then $(c, f(c))$ is an inflection point of $f$. (b) If $f'(x) < 0$ for all $x$ then $f(x)$ is a decreasing function everywhere. (c) If $f''(x) > 0$ for all $x$ then $f'(x)$ is an increasing function everywhere. (d) If $f'(c) = 0$ then $f(c)$ is either a local maximum or local minimum value. (e) If $f(x)$ is an increasing function then $f'(x)$ is an increasing function.

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Problem 3. Determine whether each of the following statements is TRUE or FALSE. (a) If f^(')(c)=f^('')(c)=0 then (c,f(c)) is an inflection point of f. TRUE FALSE (b) If f^(')(x)=0 for all α then f^(2)(x) is a decreasing function everywhere. TRUE FALSE (c) If f'(x)>0 for all x then f^(')(x) is an increasing function everywhere. TRUE FALSE (d) If f^(')(c)=0 then f(c) is either a local maximum or local minimum value. TRUE FALSE (e) If f(x) is an increasing function then f^(2)(x) is an increasing function. TRUE FALSE Problem 3. Determine whether each of the following statements is TRUE or FALSE. (a) If f^(')(c)=f^('')(c)=0 then (c,f(c)) is an inflection point of f. TRUE FALSE (b) If f^(')(x)=0 for all α then f^(2)(x) is a decreasing function everywhere. TRUE FALSE (c) If f'(x)>0 for all x then f^(')(x) is an increasing function everywhere. TRUE FALSE (d) If f^(')(c)=0 then f(c) is either a local maximum or local minimum value. TRUE FALSE (e) If f(x) is an increasing function then f^(2)(x) is an increasing function. TRUE FALSE

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