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# Functions

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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
+113118
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the Latex is not displaying so I will add a pic of my preview:

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(1)=\frac{sin(a)}{b}=0\\
so,\\ sin(a)=0\\

Apr 25, 2021
edited by Melody  Apr 25, 2021
#3
+272
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Thanks a ton for this explanation :D

amygdaleon305  Apr 25, 2021
#4
+113118
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You are welcome.

Melody  Apr 25, 2021
#5
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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
+113118
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Apr 25, 2021