Suppose that f ( x ) = x ? x ? ln( x ). Answer the following questions. Give exa

Question

Suppose that f(x) = x ? x?ln(x). Answer the following questions. Give exact symbolic answers. Do not use decimals. Where does f(x) have a horizontal tangent? x = Where does f?'(x) = ?4? x = Assuming k is a constant, where does f?'(x) = k?? x =
Suppose that f(x) = x ? x?ln(x). Answer the following questions. Give exact symbolic answers. Do not use decimals. f(x) = x ? x?ln(x). Where does f(x) have a horizontal tangent? f(x) x = x = Where does f?'(x) = ?4? f?'(x) = ?4? x = x = Assuming k is a constant, where does f?'(x) = k?? f?'(x) = k?? x =
x =

Explanation / Answer

as given f(x) = x - xlnx

f'(x) = 1 - (lnx + x*(1/x)) = 1 - lnx -1 = -lnx ------------- (using d(uv) = v.du + u.dv)

now for first part

f'(x) = 0

-lnx = 0 or x =1

ans x = 1

for second part

f'(x) = -4

-lnx = -4

lnx = 4

x = e^(4)

ans x = e^(4)

for third part

f'(x) = k

-lnx = k

lnx = -k

x = e^(-k)

ans x = e^(-k)

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