Mathematics Integration Level: Misc Level

Find the (absolute) maximum and the (absolute) minimum values of the following function in the indicated intervals. Also find the points of (absolute) maxima and minima

f(x) = (x-1)^{2} + 3 in [-3,1]

Mathematics Integration Level: Misc Level

Find the maximum and the minimum values (if any) of the following function

f(x) = Sin 2x + 5

Mathematics Integration Level: Misc Level

Find the maximum and the minimum values (if any) of the following function

f(x) = |x + 2| - 1

Mathematics Integration Level: Misc Level

Find the maximum and the minimum values (if any) of the following function

f(x) = - (x-1)^{2} + 10

Mathematics Integration Level: Misc Level

Find the interval in which f(x) = x^{2}e^{-x} is increasing

Mathematics Integration Level: Misc Level

Find the interval in which the following function is strictly increasing or strictly decreasing

f(x) = x^{4} - 4x

Mathematics Integration Level: Misc Level

Find the interval in which the following function is strictly increasing or strictly decreasing

Mathematics Integration Level: Misc Level

Find the interval in which the following function is strictly increasing or strictly decreasing

f(x) = 2x^{3} - 3x^{2} - 36x + 7

Mathematics Integration Level: Misc Level

Find the interval in which the following function is strictly increasing or strictly decreasing

f(x) = x^{2} - 4x + 6

Mathematics Integration Level: Misc Level

Prove that the function f given by is increasing in

Mathematics Integration Level: Misc Level

Prove that the function f given by f(x) = Sin x is

(i) strictly increasing on

(ii) strictly decreasing on

(iii) neither increasing nor decreasing in (0,)

Mathematics Integration Level: Misc Level

Prove that the function f given by f(x) = log Cos x is strictly decreasing on

Mathematics Integration Level: Misc Level

Show that the function f given by f(x) = x3 - 3x2 + 4x, xR, is strictly increasing on R

Mathematics Integration Level: Misc Level

Show that the function f(x) = log x is strictly increasing

Mathematics Integration Level: Misc Level

Show that the function f(x) = 7x -3 is strictly increasing on R