Calculus

Application of Derivatives

Easy

The tangent to the curve $y = e^{3x}$ at the point $(0, 1)$ , meets the x-axis at :

$(0, 1)$

$(0, 3)$

$\left(-\frac{1}{3}, 0\right)$

$\left(\frac{1}{3}, 0\right)$

✅ Correct Option: 3

$\frac{dy}{dx} = 3e^{3x}$ . At $(0,1)$ , slope $= 3$ . Tangent: $y - 1 = 3(x - 0)$ , i.e. $y = 3x + 1$ . For x-axis, $y = 0 \Rightarrow x = -\frac{1}{3}$ . Point is $\left(-\frac{1}{3}, 0\right)$ .

2025: 3 June Shift 2

The demand for a certain product is represented by the function

$p = 150 + 10x - x^2$ (in Rs.)

where $x$ is the number of units demanded and $p$ is the price per unit, then the value of marginal revenue, when 10 units are sold is

2026: 26 May Shift 2

If a manufacturer's total cost 'C' is given by $C = \dfrac{x^2}{25} + 3x$ , then the marginal cost when 7 units are produced will be:-

2025: 3 June Shift 2

Which of the following functions has a local minima at $x = 0$ ?

(A) $f(x) = x^3$

(B) $f(x) = |x|$

(D) $f(x) = x^{-2}$

Choose the correct answer from the options given below:

2026: 18 May Shift 2

For the function $f(x)=2x^3-21x^2+36x-100$ ;

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. Point of local maxima is	I. -208
B. Point of local minima is	II. -83
C. Local maximum value is	III. 6
D. Local minimum value is	IV. 1

Choose the correct answer from the options given below:

2022: 6 Aug Shift 2

The slope of normal to the curve $y = 3x^2 + 3 \sin 3x$ , at $x = 0$ is:

2022: 23 Aug Shift 1

Sumit's position, when $x = 10$ is :

The tangent to the curve y=e3xy = e^{3x}y=e3x at the point (0,1)(0, 1)(0,1), meets the x-axis at :

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

The tangent to the curve $y = e^{3x}$ at the point $(0, 1)$ , meets the x-axis at :