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The graph of the function \( f(x)={sin(ax)\over bx}\) passes through a point (1,0). The coefficient of the direction of the tangent to the graph of the function at the point (\(1 \over 4\),\(f({1 \over 4})\)) is -4. Determine the value of parameters \(a\epsilon <4,7>\) and \(b\).

Sorry for my English. Tried my best to translate :P

 Apr 22, 2021
 #1
avatar+113118 
+2

the Latex is not displaying so I will add a pic of my preview:

 

 

\(f(x)=\frac{sin(ax)}{bx}\qquad b\ne 0,\quad x\ne0\quad 4

 

Now at x=0.25 the gradient will be -4

 

so you need to differentiate this, then substitute in x=0.25 

then solve for b given that f(0.25)=-4

 

Now you try it from there.

 

 

 

 

 

 

Coding:

f(x)=\frac{sin(ax)}{bx}\qquad b\ne 0,\quad x\ne0\quad 4 f(1)=0\\
f(1)=\frac{sin(a)}{b}=0\\
so,\\ sin(a)=0\\
a=n\pi\qquad n\in Z\\
\text{but}\quad 4 a=2\pi\\
f(x)=\frac{sin(2\pi x)}{bx}\qquad b\ne 0,\quad x\ne0\

 Apr 25, 2021
edited by Melody  Apr 25, 2021
 #3
avatar+272 
+1

Thanks a ton for this explanation :D

amygdaleon305  Apr 25, 2021
 #4
avatar+113118 
+1

You are welcome.   laugh

Melody  Apr 25, 2021
 #5
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+1

Thank you so much! I've started doing derivations and this was bothering me as h**l, sadly my teacher has no time to explain extra tasks! Cheers man!

Guest Apr 27, 2021
 #2
avatar+113118 
+2
 Apr 25, 2021

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