MHB Master Calculus Questions with Expert Tips | Boost Your Grades

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[HOI]

For problem 8, $f(x)=\sqrt{3x+25}$ which can be written as $f(x)=(3x+25)^{1/2}$. Now I suppose you know that the derivative of $x^n$ is $nx^{n- 1}$ (here n= 1/2) and that, by the chain rule, the derivative of $(g(x))^n= n(g(x))^{n-1} g'(x)$ (here g(x)= 3x+ 25 and g'(x)= 3).

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.