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In summary, for problem 8, we have $f(x)=\sqrt{3x+25}$, which can also be written as $f(x)=(3x+25)^{1/2}$. The derivative of $x^n$ is $nx^{n-1}$, and using the chain rule, the derivative of $(g(x))^n= n(g(x))^{n-1} g'(x)$, where in this case, g(x)=3x+25 and g'(x)=3.Moving on to problem 9, the slope of the tangent line is 8, but the value of the function $f(-1)$ is incorrect. It should be $-4(-1)^2

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For problem 9, yes, the slope of the the tangent line is 8. But you have the value of the function wrong! $f(-1)= -4(-1)^2$. That is NOT 4! (Look at the difference between $(-1)^2$ and $-1^2$.)

For problem 10 you have correctly found that the derivative is -2x+ 5 but you have left the next part, the slope of the tangent line at x=2, blank. Why is that? Do you not understand that the slope of the tangent line at a given x is the derivative at that x? Here that is -2(2)+5.

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