Question

find the local maxima and local minima if any, of the following functions. Find also the local maximum and local minimum values, as the case may be
f(x) = sinx - cosx ,0<x<2n​

Answer 1

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Step-by-step explanation:

The points for which f

′

(x)=0 or DNE are the points of local minima or local maxima

f(x)=sinx−cosx

dx

d(f(x))

=

dx

d(sinx−cosx)

f

′

(x)=cosx+sinx

For, f

′

(x)=0, tanx=−1

Since, x∈(0,2π), x=135

o

Now, Let's find this vlaue of local maxima or minima

f(135

o

) = sin(135

o

)−cos(135

o

)=

2

1

−

2

−1

=

2