Question

Find the maximum and minimum value of f[x]=3cosx+4sinx

Answer 1

Step-by-step explanation:

We have,

$f(x) = 3 \cos(x) + 4 \sin(x)$

$= > f(x) = 5( \frac{3}{5} \cos(x) + \frac{4}{5} \sin(x) )$

Let sin(y) = 3/5 and cos(y) = 4/5

so,

$= > f(x) = 5( \sin(y) \cos(x) + \cos(y) \sin(x) )$

$= > f(x) = 5 \sin(y + x)$

We know that, -1 ≤ sin(x) ≤ 1

so,

$- 1 \leqslant \sin(y + x) \leqslant 1$

$= > - 5 \leqslant 5 \sin(y + x) \leqslant 5$

$= > - 5 \leqslant f(x) \leqslant 5$

Hence, maximum and minimum values of f(x) are 5 and -5