"For which values of f ( x )..." was answered by our experts

caschaillo7

Answered question

2022-11-01

For which values of

f (x) = m x

intersect the function

g (x) = \log x

lefeuilleton42

Beginner2022-11-02Added 12 answers

There will be some

m_{0}

for which

m_{0} x

intersects

\log x

exactly once. So the answer is, the set of

m \leq m_{0}

are the

m

for which

m x

crosses

\log x

(this comes from looking at a picture). To find

m_{0}

, find the equation for the tangent line of

\log x

at each point

x_{0}

, then see which tangent line has a

y

-intercept of

0

Nikolai Decker

Beginner2022-11-03Added 3 answers

For

m \leq 0

, it is clear (why?) that an intersectoin occurs. For

m > 0

first answer the question: For which value of

m

is the line

y = m x

a tangent line to the graph of

g

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