Is f(x)=-3x^5-2x^4-9x^2+x-7 concave or convex at x=5? Calculus Graphing with the Second Derivative Analyzing Concavity of a Function 1 Answer SCooke Dec 18, 2017 f’’(5) = -8118 Less than zero, therefore concave. Explanation: f’’(x) < 0 at x = 5 (concave) f’’(x) > 0 at x = 5 (convex) f’(x)=-15x^4-8x^3-18x+1 f’’(x)=-60x^3-24x^2-18 f’’(5)=-60(125)-24(25)-18 = -8118 Less than zero, therefore concave. 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 1183 views around the world You can reuse this answer Creative Commons License