The point on the curve $y=-x^2+12x+5$ wh

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Applications of Derivatives

Question:

The point on the curve $y=-x^2+12x+5$ where the tangent is parallel to the x-axis is :

Options:

(-6, -103)

(6, 41)

(0, 5)

(6, 103)

Correct Answer:

(6, 41)

Explanation:

The correct answer is option (2) → (6, 41) $\frac{80}{89}$

$y=-x^2+12x+5$ ...(I)

$\frac{dy}{dx}=-2x+12$

tangent parallel to x-axis

$⇒\frac{dy}{dx}=0⇒x=6$

from (I) $y=-(6)^2+12(6)+5$

$=-36+72+5=41$

P(6, 41) at which tangent parallel to x-axis