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# Tutor profile: Tim S.

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Tim S.
Tutor for many years
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## Questions

### Subject:Linear Algebra

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Question:

Find the inner product of the vector \$\$(1, 2, 5)\$\$ with \$\$(5, 2, 7)\$\$.

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Tim S.

To find the inner product we multiply the corresponding components of each vector and then sum them together. Thus, the inner product is \$\$1*5+2*2+5*7=44\$\$.

### Subject:Pre-Calculus

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Question:

Factor the polynomial \$\$x^2-5x+6\$\$ and find its roots.

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Tim S.

We can factor the polynomial as \$\$(x-2)(x-3)\$\$. To find the roots we set each factor equal to \$\$0\$\$. So \$\$x-2=0\$\$ and \$\$x-3=0\$\$. Solving these two equations we find the roots are \$\$x=2\$\$ and \$\$x=3\$\$.

### Subject:Calculus

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Question:

Find the derivative of the function \$\$f(x) = x^2\$\$.

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Tim S.

To find the derivative of \$\$x^2\$\$ we use the power rule. The power rule states that if \$\$f(x) = x^n\$\$ then the derivative is \$\$f'(x)=nx^{n-1}\$\$. Thus using the power rule if \$\$f(x)=x^2\$\$ then \$\$f'(x)=2x\$\$.

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