Answer :
The slope of the tangent is equal to zero when the derivative is equal to zero, in other words when the function attains a local extremum (maximum or minimum)
So we have to ask ourselves, at which "x" value does f(x) admit a maximum or minimum.
From the graph we can tell that it is at the point of abscissa 2
Answer: x=2
Final answer:
The x-value at which the slope of the tangent line to the curve is zero is found by taking the derivative of the function, setting it equal to zero, and solving for x.
Explanation:
In mathematics, the slope of the tangent line to the curve at a point is obtained by finding the derivative of the function at that point. When the slope of the tangent line is zero, this corresponds to a horizontal tangent. Therefore, we are essentially looking for the x-values at which the derivative of the function is equal to zero.
Assuming that the function and its derivative are known, you find the derivative and set it equal to zero.
Then solve for x. For example, if your function is f(x) = x2 - 3x + 2, its derivative f'(x) = 2x - 3. Setting this equal to zero gives x = 3/2. Thus, the slope of the tangent line to the curve f(x) = x2 - 3x + 2 is zero at x = 3/2.
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