Application of Derivatives Practice Questions

JEE · Mathematics · 1505 free MCQs with instant results and detailed explanations.

1505

Total

361

Easy

678

Medium

466

Hard

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Topics in Application of Derivatives

Monotonicity 221

Tangent and Normal 221

Maxima and Minima 288

Rate of Change 237

Rolle's Theorem 305

Mean Value Theorem 233

Sample Questions from Application of Derivatives

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Easy

If the curve y = sin x has a tangent line at x = π/4, what is the slope of the tangent line?

A. √2/2

B. 1

C. √3/2

D. 0

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Correct Answer: A

The derivative of y = sin x is dy/dx = cos x. At x = π/4, cos(π/4) = √2/2.

Easy

What is the slope of the tangent line to the curve y = ln(x) at x = 1?

A. 1

B. 0

C. ∞

D. e

Show Answer & Explanation

Correct Answer: A

The derivative of y = ln(x) is 1/x. At x = 1, the slope is 1/1 = 1.

Easy

If f(x) = ln(x), what is the rate of change at x = 1?

A. 0

B. 1

C. undefined

D. e

Show Answer & Explanation

Correct Answer: B

The derivative f'(x) = 1/x. At x = 1, f'(1) = 1/1 = 1.

Medium

For the curve y = x + sin(x), what is the equation of the tangent at x = 0?

A. y = x

B. y = x + 1

C. y = x - 1

D. y = 1

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Correct Answer: A

At x = 0, the value of sin(0) = 0 and the slope is 1. Thus, the equation is y = x.

Medium

At which point does the curve y = e^x have a normal that is horizontal?

A. x = 0

B. x = 1

C. x = -1

D. None of the above

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Correct Answer: D

Since the derivative of e^x is never zero, the normal can never be horizontal.

Medium

The angle between the tangent to the curve y = x^2 and the x-axis at the point (2,4) is:

A. 45 degrees

B. 30 degrees

C. 60 degrees

D. 90 degrees

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Correct Answer: A

The slope at (2,4) is 4. The angle θ = tan^(-1)(slope) = tan^(-1)(4).

Medium

For the curve y = tan(x), at what x-coordinate does the tangent line have a slope of 1?

A. π/4

B. 0

C. π/2

D. 3π/4

Show Answer & Explanation

Correct Answer: A

The slope is given by the derivative, and we set the derivative equal to 1 to find x.

Hard

Find the coordinates where the normal to the curve y = x^2 + 2x intersects the x-axis.

A. (-1, 0)

B. (1, 0)

C. (0, 0)

D. (0, 1)

Show Answer & Explanation

Correct Answer: A

To find the normal, first find the derivative dy/dx = 2x + 2. The slope at x = -1 is 0. The normal line will intersect the x-axis at x = -1.

Hard

The curve y = ln(x) has a tangent at (1, 0). What is the slope of that tangent?

A. 1

B. 0

C. 2

D. e

Show Answer & Explanation

Correct Answer: A

The derivative of y = ln(x) is 1/x. At x = 1, the slope is 1/1 = 1.

Q10

Hard

If the normal to the curve y = x^2 + 2x at the point (1, 3) meets the x-axis at point P, find the x-coordinate of P.

A. -1

B. 0

C. 1

D. 2

Show Answer & Explanation

Correct Answer: A

The slope of the normal is the negative reciprocal of the slope of the curve at that point. Compute slope at (1, 3) and use point-slope form to find where it meets the x-axis.

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Application of Derivatives — JEE Mathematics Practice Questions Online

This page contains 1505 practice MCQs for the chapter Application of Derivatives in JEE Mathematics. The questions are organized by difficulty — 361 easy, 678 medium, 466 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 6 topics, giving you comprehensive coverage of the entire chapter.