Q1 of 168 Page 205

Show that the function given by f (x) = 3x + 17 is strictly increasing on R.

Let x₁ and x₂ be any two numbers in R.

Then, we have,

x₁ < x₂

⇒ 3x₁ < 3x₂

⇒ 3x₁ +17 < 3x₂ +17

⇒ f(x₁) < f(x₂)

Therefore, f is strictly increasing on R.

The rate of change of the area of a circle with respect to its radius r at r = 6 cm is

The total revenue in Rupees received from the sale of x units of a product is given by

R(x) = 3x² + 36x + 5. The marginal revenue, when x = 15 is

Show that the function given by f (x) = e^2x is strictly increasing on R.

Show that the function given by f (x) = sin x is

(a) strictly increasing in