Find the slope of tangent to Y = [tex]4 \div x + 2 \sqrt{x} [/tex]at x=4
Accepted Solution
A:
Answer:slope = [tex]\frac{1}{4}[/tex]Step-by-step explanation:To find the slope, differentiate with respect to x and evaluate at x = 4[tex]\frac{dy}{dx}[/tex] is the measure of the slope of the tangent at x = aDifferentiate each term using the power rule[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]Giveny = [tex]\frac{4}{x}[/tex] + 2[tex]\sqrt{x}[/tex] = 4[tex]x^{-1}[/tex] + 2[tex]x^{\frac{1}{2} }[/tex], hence[tex]\frac{dy}{dx}[/tex] = - 4[tex]x^{-2}[/tex] + [tex]x^{-\frac{1}{2} }[/tex][tex]\frac{dy}{dx}[/tex] = - [tex]\frac{4}{x^{2} }[/tex] + [tex]\frac{1}{\sqrt{x} }[/tex]At x = 4[tex]\frac{dy}{dx}[/tex] = - [tex]\frac{4}{16}[/tex] + [tex]\frac{1}{\sqrt{4} }[/tex] = - [tex]\frac{1}{4}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{4}[/tex]