Q35 of 105 Page 17

Find the value(s) of a for which f(x) = – ax is an increasing function on R ?

We have,

f(x) = – ax

Given that f(x) is on increasing function

for all x R

⇒ for all x R

⇒ a < for all x R

But the last value of 3x² = 0 for x = 0

∴a ≤ 0

33 Prove that the function f(x) = cos x is :

i. strictly decreasing on (0, π)

ii. strictly increasing in (π, 2π)

iii. neither increasing nor decreasing in (0, 2 π)

Show that f(x) = – x sin x is an increasing function on (0, π/2) ?

Find the values of b for which the function f(x) = sin x – bx + c is a decreasing function on R ?

Show that f(x) = x + cos x – a is an increasing function on R for all values of a ?