2.8 Homework - The Derivative as a Function (Homework)

6. [-/1 Points] DETAILS SCALCET9 2.8.032. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the derivative of the function using the definition of derivative. g( x ) = 8+Vx g '(x ) = State the domain of the function. (Enter your answer using interval notation.) State the domain of its derivative. (Enter your answer using interval notation.) Need Help? Read It 7. [-/1 Points] DETAILS SCALCET9 2.8.041. MY NOTES ASK YOUR TEACHER The graph of fis given. State the numbers at which f is not differentiable. (Enter your answers as a comma-separated list.) X Need Help? Read It8. [-/1 Points] DETAILS SCALCET9 2.8.047.EP. MY NOTES ASK YOUR TEACHER The graphs of a function f and its derivative f' are shown. The graph of fhas a [-Select- Vy-intercept. The value of f'(-1) is [--Select... V because [--Select-.. The value of f"(1) is [--Select-- V because ---Select--- -Select- Which is bigger, f'(-1) or f"(1)? is concave downward at x = OF(-1) f is concave upward at x = 1 f is increasing at x = 1 Of(1) the graph of f' is above the x-axis at x = 1 "is decreasing at x = 1 Need Help? Read It Submit Answer9. [-/1 Points] SCALCET9 2.8.055. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER DETAILS If f(x) = 2x2 - x3, find f' (x), f"(x), f"(x), and f(4)(x). F' (x ) F " ( x ) = FI ( x ) = F ( 4) ( x ) = Graph f, f', f", and f on a common screen. 10 10 10 10 5 -4 -2 -6 -4 -2 -6 -4 -2 6 -4 -2 -6 -10 10 -10 Are the graphs consistent with the geometric interpretations of these derivatives? The graphs ---Select--- V consistent with the geometric interpretations of the derivatives because ' ---Select-- where fhas a slope of m = 0, f" [-Select-.. where f' has a slope of m = 0, and f" is [-Select- V function equal to the slope of f". -Select-- Need He are are not Watch it Submit Answer10. [-/1 Points] DETAILS SCALCET9 2.8.068.EP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Let { be the tangent line to the parabola y = 3x2 at the point (1, 3). The angle of inclination of f is the angle @ that f makes with the positive direction of the x-axis. Find y'. Find the slope m of the tangent line at the point (1, 3). m= Calculate to the nearest degree. Need Help? Read It