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

Find the maximum and minimum value, if any, of the following function given by g(x) = − |x + 1| + 3.

Find the maximum and minimum value, if any, of the following function given by h(x) = sin(2x) + 5.

Find the maximum and minimum value, if any, of the following function given by f(x) = |sin 4x + 3|

Find the maximum and minimum value, if any, of the following function given by h(x) = x + 1, x ∈ (−1, 1)

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

f(x) = x²

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

g(x) = x³ − 3x

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

`h(x) = sinx + cosx, 0 < x < pi/2`

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

f(x) = sinx − cos x, 0 < x < 2π

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

f(x) = x³ − 6x² + 9x + 15

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

`g(x) = x/2 + 2/x, x > 0`

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

`g(x) = 1/(x^2 + 2)`

Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be:

`f(x) = xsqrt(1-x), x > 0`

Prove that the following function do not have maxima or minima:

f(x) = e^x

Prove that the following function do not have maxima or minima:

g(x) = logx

Prove that the following function do not have maxima or minima:

h(x) = x³ + x² + x + 1

Find the absolute maximum value and the absolute minimum value of the following function in the given interval:

`f(x) =x^3, x in [-2,2]`

Find the absolute maximum value and the absolute minimum value of the following function in the given interval:

f (x) = sin x + cos x , x ∈ [0, π]

Find the absolute maximum value and the absolute minimum value of the following function in the given interval:

`f(x) = 4x - 1/x x^2, x in [-2 ,9/2]`

Find the absolute maximum value and the absolute minimum value of the following function in the given interval:

f (x) = (x −1)² + 3, x ∈[−3, 1]

Find the maximum profit that a company can make, if the profit function is given by p(x) = 41 − 72x − 18x².