Ward R.
asked 11/03/20I need help I got it wrong
given: f(x)=x^2, and f(x+h)-F(x)/h and simplify
a.h
b.2x+1
c.2x+h
2 Answers By Expert Tutors
Inactive Tutor answered 11/04/20
f( x + h) - f(x) ⁄ h = [ ( x + h ) ^ 2 - x ^ 2 ] / h
= ( x 2 + 2 h x + h 2 - x 2 ) ⁄ h
= ( 2 h x + h2 ) ⁄ h
= 2 x + h
Inactive Tutor answered 11/03/20
Given f(x) = x^2. Therefore, f(x+h) = x^2+2xh+h^2.
f(x+h)+f(x) = x^2+2xh+h^2 - x^2 = 2xh+h^2
Therefore [f(x+h)+f(x)]/h = (2xh+h^2) / h = 2x+h.
Hope that makes sense.
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Inactive Tutor
Hi Ward R. did this problem give any bounds for the F(x)? Without the bounds I end up with the following equation: x^2 +2xh + h^2 - (x^3)/(3h) This result is close to one of the answers but the x^2 term and the (x^3)/(3h) would have to cancel each other out.11/03/20