Final answer:
The point of inflection of the graph of the function f(x) = 8 - 5x^4 is (0, 8). The graph is concave downward for x < 0 and concave upward for x > 0.
Step-by-step explanation:
To find the point of inflection of the graph of the function f(x) = 8 - 5x^4, we need to find the second derivative and set it equal to zero.
The first derivative of f(x) is f'(x) = -20x^3 and the second derivative is f''(x) = -60x^2.
Setting f''(x) = 0, we get -60x^2 = 0, which implies x = 0.
So, the point of inflection is (0, 8).
The graph of the function f(x) = 8 - 5x^4 is concave upward when the second derivative is positive, and concave downward when the second derivative is negative.
Since f''(x) = -60x^2, it is negative for x values less than 0 and positive for x values greater than 0.
Therefore, the graph is concave downward for x < 0 and concave upward for x > 0.