The equation of a curve is $y = 5x^2 - 7x + k$, where $k$ is a constant. Write down an expr

Question

The equation of a curve is $y = 5x^2 - 7x + k$, where $k$ is a constant. Write down an expression for $\frac{\mathrm{d}y}{\mathrm{d}x}$. The equation of the tangent to the curve at $x = p$ is $y + 2x = 3$. Find the values of $p$ and $k$.

Accepted Answer

(i) $\dfrac{\mathrm{d}y}{\mathrm{d}x}=10x-7$ (ii) $p=\dfrac12,\ k=\dfrac{17}{4}$

Differentiation - Tangents and Normals at a Point

Differentiation - Tangents and Normals at a Point

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