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Question
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
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Solution
\[\text{ Slope of the tangent } =f'(x)\]
\[ = \frac{d}{dx}\left( 2 x^6 + x^4 - 1 \right)\]
\[ = 2\frac{d}{dx}\left( x^6 \right) + \frac{d}{dx}\left( x^4 \right) - \frac{d}{dx}\left( 1 \right)\]
\[ = 12 x^5 + 4 x^3 \]
\[ \therefore \text{ Slope of the tangent at }x=1:\]
\[12 \left( 1 \right)^5 + 4 \left( 1 \right)^3 = 12 + 4 = 16\]
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