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Extension: Get the Gizmo ready: The second Select Show second derivative. derivative . Check that Show derivative is selected. The second derivative of f(x) is the derivative of the first derivative f(x). So, in other words, the second derivative f(x) is the rate at which f(x) is changing. When the 2nd derivative is negative, the graph of y = f(x) is "concave down," and when it is positive, the graph is "concave up." 1. Be sure you have 3 graphs showing in the Gizmo now. Red is the given function (y = f(x)), light blue is the first derivative (y = f(x)), and green is the second derivative (y = f (x)). A. Select Linear function. Vary a and b. In general, what is the 2nd derivative of a linear function of the form f(x) = ax + b? f"(x) = what did f '(x) B. Select Absolute value function. Vary a and b. In general, what is the 2nd derivative of f(x) = alx| + b? f"(x)=. what did f'(x) C. Select Quadratic function. Vary a, b, and c. In general, what is the 2nd derivative of f(x) = ax2 + bx + c? f"(x) = what did f'(x) D. Select Cubic function. Vary a, b, c, and d. In general, what is the 2nd derivative of f(x) = ax3 + bx2 + cx + d? f"(x) = what did f '(x) E. Select Sine function. What is the 2nd derivative of f(x) = sin(x)? f"(x) = What is the 2nd derivative of f(x) = a sin(bx) + c? f"(x) = 2. Find the first and second derivatives of each function. Check your answers in the Gizmo. A. f(x) = -4x + 5 f ( x ) = f (x) = B. f(x) = 2x2 - 3x + 4 f ( x ) = f (x) = C. f(x) = 5x3 + 0.5x2 + x - 3 f(x) = f (x) = D. f(x) = -3 sin(2x) - 4 f (x) = f (x) =3. Find the derivative x) of each function fix). Then check your answers in the Gizmo. A. If x) = 3 sin(x), then f(x) = B. If x) = sin(4x) + 5. then f(x) = C. If x) = 2 sin(0.5x) 3, then f'(x) =