Question:
Slope of the tangent to the curve $y = 9x^{2} + 7x^{4} + 5$ at the point $x = 1$ is
Slope of the tangent to the curve $y = 9x^{2} + 7x^{4} + 5$ at the point $x = 1$ is
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Slope = Derivative. Just differentiate and plug in the x-coordinate.
Updated On: May 5, 2026
- 28
- 16
- 46
- 1/46
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The Correct Option is C
Solution and Explanation
Step 1: Concept
The slope of the tangent to a curve at a point is the value of the derivative $dy/dx$ at that point.
Step 2: Meaning
Find the general derivative $y' = \frac{d}{dx}(9x^{2} + 7x^{4} + 5)$.
Step 3: Analysis
$y' = 18x + 28x^{3}$. At $x = 1$, $y'(1) = 18(1) + 28(1)^{3} = 18 + 28$.
Step 4: Conclusion
$18 + 28 = 46$. The slope is 46.
Final Answer: (C)
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