Question

the function f(x)=cosx-sinx has maximum and minimum value at x=​

Answer 1

For minimum=0
For maximum=30
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Answer 2

Answer:

The maximum value of the function $f(x)=cosx-sinx$ is 0

explanation:

• The maximum and minimum point of a function is the points where the function neither increase nor decrease

• For a maximum point of a function Y, the second derivative of the function is greater than zero, ($\frac{d^{2}Y }{dx^{2} }$  is positive and for minimum point, it is less than zero($\frac{d^{2}Y }{dx^{2} }$ is negative)

STEP 1

The given function is $f(x)=cosx-sinx$

the first derivative is $\frac{df(x)}{dx} =-sinx-cosx$

STEP 2

equate the first derivative to zero to get the value of x

⇒

$-sinx-cosx=0\\-cosx= sinx$

⇒

$sinx/cosx=-1\\tanx=-1\\x=-45$

STEP 3

put the value of x we get

$f(-45)=cos(-45)-sin(-45)=0$

which is the maximum value of the function