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WWGD

Science Advisor

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A friend asked me to help him with this; probably simple, but I seem to be missing

something obvious:

For what values of ##b## is the line ##y=10x## tangent to the curve ##C(x)=e^{bx}##?

Seems we need ##C'(x)=be^{bx} =10 ## for some pair ##(b,x)##. But this is where it

seems hairy: how do we isolate either ## b ## or ##10## ? we can apply ##ln## on both

sides of ## C'(x)## , to get ## bx =ln(10/b)=ln10-lnb ## . Then what?

something obvious:

For what values of ##b## is the line ##y=10x## tangent to the curve ##C(x)=e^{bx}##?

Seems we need ##C'(x)=be^{bx} =10 ## for some pair ##(b,x)##. But this is where it

seems hairy: how do we isolate either ## b ## or ##10## ? we can apply ##ln## on both

sides of ## C'(x)## , to get ## bx =ln(10/b)=ln10-lnb ## . Then what?

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