Homework SourseUse the definition of the derivative to find f 0 if f x x
Use the definition of the derivative to find f \'(0) if f ( x ) = x^8 + x - 7 (note: you are not
asked to find a general formula for f \' ( x ) )
asked to find a general formula for f \' ( x ) )
Solution
f \' ( x ) = f(x+h) - f(x) /h where h--> 0 f(x) = x^8 + x - 7 f \' (X) = f(x+h) - f(x) /h f`(x) = (x+h)^8 + x+h -7 - (x^8 + x - 7) /h = [x^8 + 8x^7h + 28x^6h^2 +... + x+ h -7 -(x^8 + x - 7)]/h = putting x=0 and lt h-->0 =[8x^7h + h]/h = 8x^7 +1
