Applied Mathematics

Calculus

Medium

The value of a for which the function $f(x) = a^x$ is increasing on R are given by :

$0 < a < \infty$

$-\infty < a < \infty$

$1 < a < \infty$

$0 \leq a < \infty$

✅ Correct Option: 3

$f(x) = a^x \Rightarrow f'(x) = a^x \ln a$ .

For $f$ to be increasing on R, $f'(x) > 0$ for all x.

Since $a^x > 0$ for $a > 0$ , we need $\ln a > 0$ , i.e., $a > 1$ .

Note: We have selected option (3) based on the strict mathematical definition of increasing. The original key marks (1), but for $0 < a < 1$ the function is decreasing, so $1 < a < \infty$ is the correct range.

2024: 16 May Shift 1

A company is selling a certain commodity $x$ . The demand function for the commodity is linear. The company can sell $2000$ units when the price is ₹ $8$ per unit and it can sell $3000$ units when the price is ₹ $4$ per unit. The Marginal revenue at $x=5$ is:

2023: 11 Aug Shift 1

If $y = x^3 \log x$ , then $\frac{d^2 y}{dx^2}$ is equal to :

2023: 11 Aug Shift 1

The order and degree Of the differential equation $\frac{d^2 y}{dx^2} + 2 e^{-x} = 0$ , respectively are

2026: 30 May Shift 2

In a company, the cost of producing one item is ₹100, if the item is sold at ₹150 and ₹50,000 is the fixed cost of the company, then the break-even point is:

2023: 7 June Shift 1

The value of the integral $\int e^x \left(\frac{1}{x} - \frac{1}{x^2}\right) dx$ is :

2023: 30 May Shift 3

If $C(x) = ax^2 - bx - c$ represents the total cost function then the slope of the tangent to the marginal cost curve at the point $(x, y)$ is :

The value of a for which the function f(x)=axf(x) = a^xf(x)=ax is increasing on R are given by :

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

The value of a for which the function $f(x) = a^x$ is increasing on R are given by :