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
+118677 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\
