Thanks so much for all your help! That was way simpler than I thought, I think I was just overthinking it. Do you think you could also help me find the concave up at x = −2, x = −1, and x = 2 and show f(x) is concave down at x = 0? (this is still for the function f(x)= 3/4x^4-x^3-3x^2+6x)

Question

Thanks so much for all your help! That was way simpler than I thought, I think I was just overthinking it. Do you think you could also help me find the concave up at x = −2, x = −1, and x = 2 and show f(x) is concave down at x = 0? (this is still for the   function f(x)= 3/4x^4-x^3-3x^2+6x)

Stevex · Answer

f" = 9x^2-6x-6 f"(-2) and f"(-1) and f"(2) are all positive, so f is concave up there. f"(0) is negative, so f is concave down there. wolframalpha is your friend. See the graph of f and f" there. Note how the concavity changes where f"=0.