# SOLUTION: Determine where the graph of the function is concave up and concave down (if you need to enter use infinity or - infinity) f(x)=x^3-15x^2+12x+6 concave up concave down can so

Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: Determine where the graph of the function is concave up and concave down (if you need to enter use infinity or - infinity) f(x)=x^3-15x^2+12x+6 concave up concave down can so      Log On

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 Question 201601: Determine where the graph of the function is concave up and concave down (if you need to enter use infinity or - infinity) f(x)=x^3-15x^2+12x+6 concave up concave down can someone help please thanks Found 2 solutions by jsmallt9, RAY100:Answer by jsmallt9(3296)   (Show Source): You can put this solution on YOUR website!Concavity can be found using the second derivative. f(x)=x^3-15x^2+12x+6 f'(x) = 3x^2 -30x + 12 f''(x) = 6x -30 To find where the graph is concave up we want to find where the second derivative is positive. In other "words", solve 6x - 30 > 0 Adding 30 and then dividing by 6 we get x > 5 This tells us that the graph is concave up for all x-values that are greater than 5. Similarly we can find that the graph is concave down for all x-values that are less than 5. Answer by RAY100(1637)   (Show Source): You can put this solution on YOUR website!y= x^3 -15x^2 +12x +6 . y' = 3x^2 -30x +12 . to find vertex, set slope(y') =0 . 3x^2 -30x +12 =0 3(x^2 -10x +4) =0 . solve using quadratic eqn,,,x= 9.58,,,.417 . to find y,,,substitute in original eqn,,,,(9.58,-376.5),,,(.417,,8.47) . since this is a positive cubic,,rises to right,, 1st vertex,,,(.417,8.47) is concave down,,,and second vertex (9.58, -376.5) is concave up . checking,,,(.5,8.375) (.3,8.277),,,ok cc down (9.5,-376.4),(9.7, -376.3) ,,,,ok cc up