If $y = 4x - 5$ is a tangent to the curv

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Applications of Derivatives

Question:

If $y = 4x - 5$ is a tangent to the curve $y^2=px^3+q$ at (2, 3), then:

Options:

p = 2, q = -7

p = -2, q = 7

p = -2, q = -7

p = 2, q = 7

Correct Answer:

p = 2, q = -7

Explanation:

$\frac{dy}{dx}(2,3)=\frac{3px^2}{2y}=\frac{12p}{6}=2p$ So, 2p = 4 ⇒ p = 2 $∴\frac{dy}{dx}=4$

Also, (2, 3) lies on $y^2=px^3+q⇒9=2(2)^3+q$

⇒ q = -7