2. [-/3 Points] DETAILS TANAPCALC10 6.1.006. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following functions. G(x) = 8x4; f(x) = 16x (a) Verify that G is an antiderivative of f. O G(x) is an antiderivative of f(x) because G'(x) = f(x) for all x. O G(x) is an antiderivative of f(x) because G(x) = f(x) for all x. O G(x) is an antiderivative of f(x) because G(x) = f(x) + C for all x. O G(x) is an antiderivative of f(x) because f(x) = G(x) + C for all x. O G(x) is an antiderivative of f(x) because f'(x) = G(x) for all x. (b) Find all antiderivatives of f. (Use C for the constant of integration.) (c) Sketch the graphs of a few members of the family of antiderivatives found in part (b). y y 10 5 LX L X -10 -5 5 10 -10 - 5 5 10 -5/ -5(a) Verify that G is an antiderivative of f. O G(x) is an antiderivative of f(x) because G'(x) = f(x) for all x. O G(x) is an antiderivative of f(x) because G(x) = f(x) for all x. O G(x) is an antiderivative of f(x) because G(x) = f(x) + C for all x. O G(x) is an antiderivative of f(x) because f(x) = G(x) + C for all x. O G(x) is an antiderivative of f(x) because f'(x) = G(x) for all x. (b) Find all antiderivatives of f. (Use C for the constant of integration.) (c) Sketch the graphs of a few members of the family of antiderivatives found in part (b). y 10 5 X X -10 -5 5 10 -10 -5 5 10 -5/ -51 -10- O A y y\f3. [-/3 Points] DETAILS TANAPCALC10 6.1.007. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following functions. G(x) = =X 2x3; f(X) = 2x2 (a) Verify that G is an antiderivative of f. O G(x) is an antiderivative of f(x) because G'(x) = f(x) for all x. O G(x) is an antiderivative of f(x) because f(x) = G(x) + C for all x. O G(x) is an antiderivative of f(x) because G(x) = f(x) for all x. O G(x) is an antiderivative of f(x) because f'(x) = G(x) for all x. (b) Find all antiderivatives of f. (Use C for the constant of integration.) (c) Sketch the graphs of a few members of the family of antiderivatives found in part (b). y 10 10- 5- 5 X X -10 -5 5 10 -10 5 10 -5 -5(c) Sketch the graphs of a few members of the family of antiderivatives found in part (b). y -10 -5 X 5 10 -10 5 X 10 -5 -5/ O -10 -10 A y 10- 10/ 5- 5/ -10 -5 5 10 -10 -5 L X 5 10 -5 -5 O -10 - 10/ Need Help? Read It Watch It