CBSE Class 12-science Answered
Show that the tangents to the curve y = 2x3 – 3 at the points where x = 2 and x = – 2 are parallel.
Asked by Topperlearning User | 07 Aug, 2014, 08:27: AM
The equation of the curve is y = 2x3 – 3 …(i)
Differentiating w.r.t. x, we get
![dy over dx equals 6 straight x squared](https://images.topperlearning.com/topper/tinymce/cache/36da777a9601352735c3e4f1925185b0.png)
Now, m1 = Slope of the tangent at ![x equals 2 space comma space open parentheses dy over dx close parentheses subscript x equals 2 end subscript equals 6 cross times left parenthesis 2 right parenthesis squared equals 24](https://images.topperlearning.com/topper/tinymce/cache/d4de7a59de4aaa2ad59c320237c45c10.png)
![x equals 2 space comma space open parentheses dy over dx close parentheses subscript x equals 2 end subscript equals 6 cross times left parenthesis 2 right parenthesis squared equals 24](https://images.topperlearning.com/topper/tinymce/cache/d4de7a59de4aaa2ad59c320237c45c10.png)
and, m2 = Slope of the tangent at ![straight x equals minus 2 comma space open parentheses dy over dx close parentheses subscript straight x equals minus 2 end subscript equals 6 cross times left parenthesis minus 2 right parenthesis squared equals 24](https://images.topperlearning.com/topper/tinymce/cache/e3f5ec3e5711503440da1b7560cd4c9d.png)
![straight x equals minus 2 comma space open parentheses dy over dx close parentheses subscript straight x equals minus 2 end subscript equals 6 cross times left parenthesis minus 2 right parenthesis squared equals 24](https://images.topperlearning.com/topper/tinymce/cache/e3f5ec3e5711503440da1b7560cd4c9d.png)
Clearly, m1 = m2
Thus, the tangents to the given curve at the points where x = 2 and x = –2 are parallel.
Answered by | 07 Aug, 2014, 10:27: AM
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