26. (a). Find all critical points of f(x) =x 4 + ax 2 + b. (b). Under what condi

Question

26. (a). Find all critical points of f(x) =x4 + ax2 + b.       (b). Under what conditions ona and b does this function have exactly onecritical             Point? What is the one critical point, and is it a local maximum, alocal             minimum, or neither?        (c). Under whatconditions on a and b does this function haveexactly three critical              points? What are they? Which are local maxima and which are localminima?         (d). Is it everpossible for this function to have two critical points? Nocritical               points? More than three critical points? Give an explanation ineach case. 26. (a). Find all critical points of f(x) =x4 + ax2 + b.       (b). Under what conditions ona and b does this function have exactly onecritical             Point? What is the one critical point, and is it a local maximum, alocal             minimum, or neither?        (c). Under whatconditions on a and b does this function haveexactly three critical              points? What are they? Which are local maxima and which are localminima?         (d). Is it everpossible for this function to have two critical points? Nocritical               points? More than three critical points? Give an explanation ineach case.       (b). Under what conditions ona and b does this function have exactly onecritical             Point? What is the one critical point, and is it a local maximum, alocal             minimum, or neither?        (c). Under whatconditions on a and b does this function haveexactly three critical              points? What are they? Which are local maxima and which are localminima?         (d). Is it everpossible for this function to have two critical points? Nocritical               points? More than three critical points? Give an explanation ineach case.

Explanation / Answer

f'x = 4x*x*x + 2ax = 0 ...............................x [ 4x*x + 2a ] for a > 0 ............x=0 is the critical point ..............   12x*x + 2a ...it is maxima as a is +ve .........................c) for a > 0 ...............d) nope  

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