Determine
the multiplicity of each zero (write the number) and the number of turning
points in the graph of f(t)=t^{5}-7t^{3}+10t.

(Order your zeros from least to greatest)

t= -√ ; multiplicity-

t= -√ ; multiplicity-

t= ; multiplicity-

t= √ ; multiplicity-

t= √ ; multiplicity-

number of turning points:

f(t)=t^{5}-7t^{3}+10t

f(t)=t(t^{4}-7t^{2}+10)

f(t)=t(t^{2}-5)(t^{2}-2)=t(t+√5)(t-√5)(t+√2)(t-√2)

zeroes: t= -√5, -√2, 0, √2, √5

t=-√5
has an odd multiplicity: multiplicity of 1 (t^{2}-5)^{1}

t=-√2
has an odd multiplicity: multiplicity of 1 (t^{2}-2)^{1}

t=0
has an odd multiplicity: multiplicity of 1 (t)^{1}

t=√2
has an odd multiplicity: multiplicity of 1 (t^{2}-2)^{1}

t=√5
has an odd multiplicity: multiplicity of 1 (t^{2}-5)^{1}

number of turning points: 4 (A polynomial function of degree n has, at most, n-1 turning points.)