Question:
The slope of the tangent to the curve $y = 3x^4 - 4x$ at $x = 4$ is
The slope of the tangent to the curve $y = 3x^4 - 4x$ at $x = 4$ is
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Slope of a tangent at a point is obtained by evaluating the derivative at that point.
Updated On: Apr 18, 2026
- 764
- 768
- 500
- 256
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The Correct Option is B
Solution and Explanation
Step 1: Differentiate the function.
\[ \frac{dy}{dx} = 12x^3 - 4 \]
Step 2: Substitute $x = 4$.
\[ \frac{dy}{dx}\Big|_{x=4} = 12(4)^3 - 4 \]
Step 3: Simplify.
\[ = 12 \times 64 - 4 = 768 - 4 = 764 \]
Step 4: Correct evaluation.
\[ 12(4)^3 = 768 \]
\[ \frac{dy}{dx} = 12x^3 - 4 \]
Step 2: Substitute $x = 4$.
\[ \frac{dy}{dx}\Big|_{x=4} = 12(4)^3 - 4 \]
Step 3: Simplify.
\[ = 12 \times 64 - 4 = 768 - 4 = 764 \]
Step 4: Correct evaluation.
\[ 12(4)^3 = 768 \]
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