Find the slope of the tangent to the curve y = 3x⁴ – 4x at (i) x = 1 (ii) x = 4.

Solution

The equation of curve is
$straight y space equals space 3 straight x to the power of 4 minus 4 straight x$
$therefore space space space space dy over dx space equals space 12 straight x cubed minus 4 comma space space which space is space slope space of space tangent space to space the space curve.$
(i) At x = 1, $dy over dx space equals space 12 left parenthesis 1 right parenthesis cubed space minus space 4 space equals space 12 space minus 4 space space equals space 8$
which is required slope of tangent to the curve.
(ii) $At space straight x space equals space 4 comma space space space dy over dx space equals space 12 left parenthesis 4 right parenthesis cubed space minus space 4 space equals space 12 space cross times space 64 space minus space 4 space equals space 768 space minus space 4 space equals space space 764$
which is required slope of tangent to the curve

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Application Of Derivatives

Find the slope of the tangent to the curve y = 3x⁴ – 4x at (i) x = 1 (ii) x = 4.

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Application Of Derivatives

Find the slope of the tangent to the curve y = 3x4 – 4x at (i) x = 1 (ii) x = 4.

Some More Questions From Application of Derivatives Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find the slope of the tangent to the curve y = 3x⁴ – 4x at (i) x = 1 (ii) x = 4.