210 AP Calculus Exam problem tangent line to curve

• MHB
• karush
Gold Member
MHB
Find the slope of the tangent line to the graph of
$$f(x)=-x^2+4\sqrt{x}$$
at $x=4$

(A) $8-$
(B) $-10$
(C) $-9$
(D) $-5$
(E) $-7$

rewrite as
$f(x)=-x^2+4x^{1/2}$
then
$\dfrac{d}{dx}f(x)=-2x+\dfrac{2}{\sqrt{x}}$
then
$f'(4)=-2(4)++\dfrac{2}{\sqrt{4}}=-8+1=-7\quad (E)$

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