For what values of x is #f(x)=((5x)/2)^(2/3) - x^(5/3# concave or convex? Calculus Graphing with the Second Derivative Analyzing Concavity of a Function 1 Answer Sonnhard Jun 16, 2018 #f(x)# is concave for all #x# with #x>0# Explanation: Writing #f(x)# in the form #f(x)=(5/2)^(2/3)*x^(2/3)-x^(5/3)# then #f'(x)=(5/2)^(2/3)*2/3*x^(-1/3)-5/3*x^(2/3)# so #f''(x)=(5/3)^(2/3)*(-2/9)*x^(-4/3)-10/9*x^(-1/3)<0# Answer link Related questions How do you determine the concavity of a quadratic function? How do you find the concavity of a rational function? What is the concavity of a linear function? What x values is the function concave down if #f(x) = 15x^(2/3) + 5x#? How do you know concavity inflection points, and local min/max for #f(x) = 2x^3 + 3x^2 - 432x#? How do you determine the concavity for #f(x) = x^4 − 32x^2 + 6#? How do you find the intervals on which the graph of #f(x)=5sqrtx-1# is concave up or is concave... How do you determine where the given function #f(x) = (x+3)^(2/3) - 6# is concave up and where... How do you determine the intervals on which function is concave up/down & find points of... On what intervals the following equation is concave up, concave down and where it's inflection... See all questions in Analyzing Concavity of a Function Impact of this question 1272 views around the world You can reuse this answer Creative Commons License