Find points at which the tangent to the curve y = x3 – 3x2 – 9x +

1.	Find points at which the tangent to the curve y = x3 – 3x2 – 9x + 7 is parallel to the x-axis.
Answer» \(\frac{dy}{dx}\) = 3x² – 6x – 9, slope of the tangent since the tangent is parallel to x-axis \(\frac{dy}{dx}\)= 0 3x² – 6x – 9 = 0 3(x + 1) (x – 3) = 0, x = 3, x = -1 when x = 3, y = 27 – 27 – 27 - 7 = -20 when x = -1, y = -1 - 3 + 9 + 7 = 12 The points at which the tangent parallel to x – axis are (3, -20) and (-1, 12).

Find points at which the tangent to the curve y = x3 – 3x2 – 9x + 7 is parallel to the x-axis.

Answer»

\(\frac{dy}{dx}\) = 3x² – 6x – 9, slope of the tangent

since the tangent is parallel to x-axis \(\frac{dy}{dx}\)= 0

3x² – 6x – 9 = 0

3(x + 1) (x – 3) = 0, x = 3, x = -1

when x = 3, y = 27 – 27 – 27 - 7 = -20

when x = -1, y = -1 - 3 + 9 + 7 = 12

The points at which the tangent parallel to x – axis are (3, -20) and (-1, 12).