3. Consider the function f(x)=x32​(x3+44) with f′(x)=311​(x31​x3+8​) and f′′(x)=988​(x34​x3−1​) are given. Use these to

[answerhappygod]

3 Consider The Function F X X32 X3 44 With F X 311 X31 X3 8 And F X 988 X34 X3 1 Are Given Use These To 1 (42.82 KiB) Viewed 28 times

3. Consider the function f(x)=x32​(x3+44) with f′(x)=311​(x31​x3+8​) and f′′(x)=988​(x34​x3−1​) are given. Use these to answer the following questions. (Note: sign chart must be used!) (a) [2 marks] Determine the critical number(s) of f if any exists. (b) [5 marks ] Determine the intervals where f(x) is increasing and where it is decreasing and find the local extreme value(s) if any exists. (c) [5 marks] Determine the intervals where f(x) is concave upward and where it is concave downward and identify any inflection point(s)