Science (English Medium) Class 12 - CBSE Question Bank Solutions

Find the interval in which the following function are increasing or decreasing f(x) = x⁴ − 4x ?

Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \frac{x^4}{4} + \frac{2}{3} x^3 - \frac{5}{2} x^2 - 6x + 7\] ?

Find the interval in which the following function are increasing or decreasing  f(x) = x⁴ − 4x³ + 4x² + 15 ?

Find the interval in which the following function are increasing or decreasing  f(x) =  \[5 x^\frac{3}{2} - 3 x^\frac{5}{2}\]  x > 0 ?

Find the interval in which the following function are increasing or decreasing f(x) = x⁸ + 6x²  ?

Find the interval in which the following function are increasing or decreasing f(x) = x³ − 6x² + 9x + 15 ?

Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \left\{ x(x - 2) \right\}^2\] ?

Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = 3 x^4 - 4 x^3 - 12 x^2 + 5\] ?

Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \frac{3}{2} x^4 - 4 x^3 - 45 x^2 + 51\] ?

Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \log\left( 2 + x \right) - \frac{2x}{2 + x}, x \in R\] ?

Determine the values of x for which the function f(x) = x² − 6x + 9 is increasing or decreasing. Also, find the coordinates of the point on the curve y = x² − 6x + 9 where the normal is parallel to the line y = x + 5 ? 

Find the intervals in which f(x) = sin x − cos x, where 0 < x < 2π is increasing or decreasing ?

Show that f(x) = e^2x is increasing on R.

Show that f(x) = sin x is increasing on (0, π/2) and decreasing on (π/2, π) and neither increasing nor decreasing in (0, π) ?