Grade 12Differential Calculus
If 8f(x) + 6f(1/x) = x+ 5 and y= x²f(x), then what will be the value of dy/dx at x= - 1.
1 Answer
Kobi
8f(x) + 6f(1/x) = x+ 5 -Eq1Differenciating both sides:8f`(x)+6f`(1/x)*(-1/x^2)=1 -Eq2Put x=-1in Eq2f`(-1)*(8-6)=1f`(-1)=1/2Put x=-1 in eq1We get:f(-1)=(1+5)/14=3/7Given y= x²f(x),dy/dx=2xf(x)+x²f`(x)Evaluating at x=-1 we get-6/7 +1/2=-5/14
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