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Application Of Derivatives

Question
CBSEENMA12035057
Wired Faculty App

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

Solution

The equation of curve is
                      y = 7x3 + 11
therefore space space space space dy over dx space equals space 21 space straight x squared
At   straight x space equals space 2 comma space space space space dy over dx space equals space 21 left parenthesis 2 right parenthesis squared space equals space 21 space cross times space 4 space equals space 84
At  straight x space equals negative 2 comma space space space dy over dx space equals space 21 left parenthesis negative 2 right parenthesis squared space equals space 21 space cross times space 4 space equals space 84
therefore space space space space slopes space of space the space tangents space to space the space given space curve space straight y space equals space 7 straight x cubed plus 11 space space space space space space space space space when space straight x space equals space 2 space and space straight x space equals space minus 2 space are space equal therefore space space space space tangents space to space the space given space curve space at space the space points comma space when space straight x space equals space 2 space and space straight x space equals negative 2 space are space parallel.

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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