Q6 of 137 Page 18

Find the maximum and minimum values of f(x) = tan x – 2x.

we have

y = tanx – 2x

y’ = sec²x – 2

y’’ = 2sec²xtanx

For maxima and minima,

y’ = 0

sec2x = 2

secx = ±√2

x =

y’’() = 4 > 0

x = is the point of minima

y’’() = – 4 < 0

x = is the point of maxima

hence

max value = f() = – 1 –

min value = f() = 1 –

Show that has a maximum value at x = e

Find the maximum and minimum values of the function .

If f(x) = x³ + ax² + bx + c has a maximum at x = – 1 and minimum at x = 3. Determine a, b and c.

Prove that f(x) = sin x + √3 cos x has maximum value at x = π/6.