- #1

karush

Gold Member

MHB

- 3,267

- 4

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

$f'(4)=-2(4)++\dfrac{2}{\sqrt{4}}=-8+1=-7\quad (E)$

$$f(x)=-x^2+4\sqrt{x}$$

at $x=4$

(A) $8-$

(B) $-10$

(C) $-9$

(D) $-5$

(E) $-7$

$f(x)=-x^2+4x^{1/2}$

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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