Mathematics

Mathematics

Problem

3. Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: (i)

f(x)=x^{2}

(ii)

g(x)=x^{3}-3 x

(iii)

h(x)=\sin x+\cos x, 0<x<\frac{\pi}{2}

(iv)

f(x)=\sin x-\cos x, 0<x<2 \pi

(v)

f(x)=x^{3}-6 x^{2}+9 x+15

(vi)

g(x)=\frac{x}{2}+\frac{2}{x}, x>0

(vii)

g(x)=\frac{1}{x^{2}+2}

(viii)

f(x)=x \sqrt{1-x}, 0<x<1

(i)

f(x)=x^{2}

(ii)

g(x)=x^{3}-3 x

(iii)

h(x)=\sin x+\cos x, 0<x<\frac{\pi}{2}

(iv)

f(x)=\sin x-\cos x, 0<x<2 \pi

(v)

f(x)=x^{3}-6 x^{2}+9 x+15

(vi)

g(x)=\frac{x}{2}+\frac{2}{x}, x>0

(vii)

g(x)=\frac{1}{x^{2}+2}

(viii)

f(x)=x \sqrt{1-x}, 0<x<1

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