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Find the Slope of the Tangent to the Curve F (X) = 2x6 + X4 − 1 at X = 1. - Mathematics

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Find the slope of the tangent to the curve (x) = 2x6 + x4 − 1 at x = 1.

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Solution

\[\text{ Slope of the tangent } =f'(x)\]
\[ = \frac{d}{dx}\left( 2 x^6 + x^4 - 1 \right)\]
\[ = 2\frac{d}{dx}\left( x^6 \right) + \frac{d}{dx}\left( x^4 \right) - \frac{d}{dx}\left( 1 \right)\]
\[ = 12 x^5 + 4 x^3 \]
\[ \therefore \text{ Slope of the tangent at }x=1:\]
\[12 \left( 1 \right)^5 + 4 \left( 1 \right)^3 = 12 + 4 = 16\]

Concept: The Concept of Derivative - Algebra of Derivative of Functions
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Exercise 30.3 | Q 21 | Page 34

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