Question

Find the maximum and minimum value of 7 cos x + 24 sin x?​

Answer 1

Answer:

Maximum value of =v(49+576)=v(625)=25

Minimum value =-v(49+576)=-25

Answer 2

Given:

7cosx+24sinx

To find:

Maximum and minimum values of f(x)

Explanation:

$\sf 7cosx + 24sinx$

it can be compared to

$\boxed{\sf acosx+bsinx+c}$

Here

a=7,b=24,c=0

$\boxed{\sf maximum\: value,M=c+\sqrt{a^2+b^2}}$

substituting

$M=0^2+\sqrt{7^2+49^2}$

$= > \sqrt{49 + 576} = \sqrt{625} \\ \\ = 25 \: units$

Maximum value=25 units

$\boxed{\sf minimum\: value,m=c-\sqrt{a^2+b^2}}$

substituting

$m=0^2-\sqrt{7^2+24^2}$

$= > - \sqrt{49 + 576} = - \sqrt{625} \: \\ \\ = - 25 \: units$

Minimum value=-25 units