Show that the tangents to the curve y = 7x 3 + 11 at the points where x = 2 and x = 2 are parallel.

Q16 of 168 Page 211

Show that the tangents to the curve y = 7x³ + 11 at the points where x = 2 and
x = – 2 are parallel.

The given curve y = 7x³ + 11

Then, the slope of the tangent to the given curve at x = 4 is given by,

It is cleared that the slopes of the tangents at the points where x = 2 and x = -2 are equal.

Therefore, the two tangents are parallel.

Find the equations of the tangent and normal to the given curves at the indicated points:

x = cos t, y = sin t at t=π/4

Find the equation of the tangent line to the curve y = x² – 2x +7 which is

(a) parallel to the line 2x – y + 9 = 0

(b) perpendicular to the line 5y – 15x = 13.

Find the points on the curve y = x³ at which the slope of the tangent is equal to the y-coordinate of the point.

For the curve y = 4x³ – 2x⁵, find all the points at which the tangent passes through the origin.