Question

The point (1,1) is on the curve defined by f(x). Which of the following statements is true about the curve at the point?

a) The slope of the tangent at (1,1) is zero.
b) The curve is a parabola.
c) The second derivative of the curve is negative.
d) The curve is undefined at (1,1).

Answer 1

The statement that is true about the curve at the point (1,1) is a) The slope of the tangent at (1,1) is zero.

The answer is option ⇒a

Step-by-step explanation:

To determine the slope of the tangent at a point on a curve, we can find the derivative of the curve and evaluate it at that point. If the derivative is zero at that point, it implies that the slope of the tangent is zero. Therefore, in this case, the slope of the tangent at (1,1) is zero.

If the derivative is zero at a specific point, it means that the curve is not changing at that point, and the slope of the tangent line is therefore zero.

In this case, the statement tells us that at the point (1,1), the slope of the tangent is zero. This means that at that particular point, the curve is not getting steeper or shallower but is rather flat, or horizontal.

The answer is option ⇒a