Find the slope of the tangent at x = 1.

The condition is not given to us completely and most likely it should sound like this.

Find the slope of the tangent to the parabola y = -2x ^ 2 + 3x at the point with the abscissa x0 = 1.

Let’s remember what the slope of the tangent is equal to – right, equal to the value of the derivative of the function at this point.

That is, we need to find the derivative of the function:

y ‘= (-2x ^ 2 + 3x)’ = -4x + 3.

We are looking for what the derivative is equal to at the point x0 = 1:

y ‘(1) = -4 * 1 + 3 = -4 + 3 = -1.

We conclude that the slope of the tangent at the point with the abscissa x0 = 1 is -1.