 Hello friends and how are you all doing today? The question says show that the tangents to the curve y is equal to 7x cube plus 11 at the points where x is equal to 2 and x is equal to minus 2 are parallel. We have y is equal to 7x cube plus 11 not differentiating y with respect to x we get dy by dx equal to 21x square. Now at x is equal to 2 and x is equal to minus 2 the value of dy by dx is 21 2 square 21 into 4 gives us 84. Similarly here we have dy by dx at x equal to minus 2 equal to 21 into minus 2 square which is 21 into 4 which is equal to 84. Now we can see that slopes of the tangent at points x is equal to 2 and x is equal to minus 2 are same they both are 84 and 84 hence the tangents are parallel. This is what we were supposed to prove in the question so hope you understood the concept and enjoyed the session too have a nice day.