Question

Find the zeros of f(x)=-x³-2x²+7x-4. Then describe the behavior of the graph of f at each zero.

A. 4, -1;As x→-[infinity] , fto -∈fty. When -1 , f<0 . At x=4 , f is tangent to the x-axis, so when x>1, f→[infinity]
B. −4, 1;As x→-[infinity] , fto -∈fty. When -4 , f>0. At x=1 , f is tangent to the x-axis, so when x>1, f→-[infinity]
C. 4, −1;As x→-[infinity], fto ∈fty. When -1 , f>0.At x=4 , f is tangent to the x-axis, so when x>1, f→[infinity]
D. -4, 1;As x→-[infinity], f-∈fty. When -4 , f<0 . At x=1 , f is tangent to the x-axis, so when x>1, f→-[infinity]

Answer 1

The correct answer is option A. The zeros of the function f(x)=-x³-2x²+7x-4 are 4 and -1. The behavior of the graph at each zero is described as x approaches negative infinity, f approaches negative infinity. When x=-1, f is less than zero. When x is greater than 1, f approaches infinity.

Step-by-step explanation:

To find the zeros of f(x)=-x³-2x²+7x-4, we need to set the equation equal to zero and solve for x. So, -x³-2x²+7x-4=0. We can factor this equation to get (x-4)(x+1)(-x+1)=0. Therefore, the zeros of the function are x=4, x=-1, and x=1.

The behavior of the graph of f at each zero can be described as follows:
A. When x approaches negative infinity, f approaches negative infinity. When x=-1, f is less than zero. When x is greater than 1, f approaches infinity.
B. When x approaches negative infinity, f approaches negative infinity. When x=-4, f is greater than zero. When x is greater than 1, f approaches negative infinity.
C. When x approaches negative infinity, f approaches infinity. When x=-1, f is greater than zero. When x is greater than 1, f approaches infinity.
D. When x approaches negative infinity, f approaches negative infinity. When x=-4, f is less than zero. When x is greater than 1, f approaches negative infinity.

From the given options, option A is correct. The zeros of f(x) are 4 and -1, and the behavior of the graph of f at each zero matches the description in option A.