Is f(x)=xcosx concave or convex at x=pi/2? Calculus Graphing with the Second Derivative Analyzing Concavity of a Function 1 Answer Harish Chandra Rajpoot Jul 27, 2018 function is concave at x=\pi/2 Explanation: Given function: f(x)=x\cos x f'(x)=x(-\sin x)+\cosx =-x\sin x+\cos x f''(x)=-x(\cos x)-\sin x-\sin x f''(x)=-x\cos x-2\sin x f''(pi/2)=-\pi/2\cos (\pi/2)-2\sin (\pi/2) =0-2(1) =-2 Since f(\pi/2)<0 hence the given function is concave at x=\pi/2 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 1827 views around the world You can reuse this answer Creative Commons License