Question

Let f(x) be a differentiable function that is one-to-one. Suppose that y=−3x+8 is the equation of the tangent line to the graph y=f(x) at x=5. (a) Find f(5)

Answer 1

To find f(5) for the function that has a tangent line y=-3x+8 at x=5, substitute x=5 into the tangent line's equation to get f(5)=-7.

Step-by-step explanation:

The question asks for the value of f(5) given that the function f(x) is differentiable, one-to-one, and has a tangent line with the equation y=-3x+8 at x=5. To find f(5), we can substitute x = 5 into the equation of the tangent line since the tangent line touches the function exactly at that point. Plugging in the value, we have:

y = -3(5) + 8

y = -15 + 8

y = -7

Therefore, f(5) = -7.