Question

Can anyone help with this homework question? I will attach a document.

Answer 1

\[h(x)=4(3f(x)-g(x))^\left( 1/2 \right)\]

Answer 2

take the derivative (will be using the chain rule)

Answer 3

\[h \prime(x)=(1/2)(4)(3f(x)-g(x))^\left( -1/2 \right)(3f \prime(x)-g \prime(x))\]
now sub x=12
\[h \prime(12)=(1/2)(4)(3f(12)-g(12))^\left( -1/2 \right)(3f \prime(12)-g \prime(12))\]

Answer 4

\[h \prime (12)=2(3 * 4-8)^\left( -1/2 \right)(3*15--5)\]
\[h \prime (12)=2(12-8)^\left( -1/2 \right)(45+5)\]
\[h \prime (12)=2(4)^\left( -1/2 \right)(50)\]
\[h \prime (12)=2(1/2)(50)\]
\[h \prime (12)=(50)\]

Answer 5

Thank you!

Answer 6

I wrote the steps out to help you study it...... :)

Answer 7

Yes, that is awesome! It really helps to see it step by step.